Br. Muslim First,
You are not understanding what sis fatema is saying. Whenever I stand up to pray, my 3 year old comes and pretends to follow me. What he does though is faces me while doing ruku or sujood. So if we consider Taher Saifuddin and Mohammed Burhanuddin 3 year olds, it seems like a possibility.
Jokes apart, what the Syedna is doing, is creating idol worshippers. Consider the Syedna visiting the person in the hospital in the night and then visiting those affected by the earthquake in the night. Why does he have to do it in the night? Why can't he visit them and cure them during the day in broad daylight? Jesus Christ cured the sick and the blind right in the middle of the town in broad daylight. Prophet Mohammad performed his miracles right in the middle of all his followers. There is, however, an explanation for what the bohras have experienced. These are games played by jinns (for those who believe in them) to lead idol worshippers astray.
So I won't say that the nurse didn't see Burhanuddin, it just wasn't him. It was someone else pretending to be him. People experience these things quite often. People see Krishna coming to save them or Buddha or whoever else one trusts. With these forms it becomes easy for these beings to lead you astray. And in case of Fatema, it was a tremendous success.
Now consider some of the other points raised by sis Fatema,
1) 8th August 1986 was declared as "His Holiness Dr. Syedna Mohammed Burhanuddin Day" by the Mayor of Houston.
At that time, was the mayor of houston an authority on what is holy and what is not as per Islam? Did he even know the difference between Shias and Sunnis? It is quite obvious that this was simply an organized propaganda event.
2) At the age of 5, Syedna recited the Quran in a majlis. Subsequently Syedna Taher Saifuddin (RA) wrote in his Risalat Sharifa: When he recites the Quran he glows for the people of heaven as the stars glow for the people of earth.
The Syedna cannot recite the quran even today without assistance. And I heard on American Idol last week that one of the contestants, the one with the long hair had a glow on his head when he took the stage. It was simply because of the light shining on the gel on his head.
3) When Syedna Taher Saifuddin (RA) and Syedna Mohammed Burhanuddin (TUS) entered the precincts of the Kaaba, Syedna Taher Saifuddin (RA) asked: Where is the qibla from where I stand? Syedna Mohammed Burhanuddin (TUS) replied: You are our qibla right before us!
Again, prime example of going against the command of Allah and committing shirk. Allah has clearly mentioned in the quran that Kaaba is the qibla and not some human being.
4) On the completion of 1400 years from the day of revelation of the Quran, Syedna delivered a speech about the Quran which was heard on All India Radio.
As a Dai, it is his duty to spread the message of Islam every day. If he did this only on one occasion then he should be ashamed of himself. He should have a regular show on All India Radio talking about Islam every day. He has power and he has money. He should put it to good use instead of feeding it to the pigs.
5) Syedna's (TUS) family including grand and great grand children today number 104. His eldest great grandchild is 23 yrs of age, whilst his youngest grandchild is 3.
Now consider this family that is living on the money given to them by their followers and then consider the family of the prophet of Islam. As shias go, God loved Hazrat Hussain so much that he wanted him in heaven with Him. Then by that going God hates this guy so much that he wants him to spend his life on earth till eternity. Now, the bohras will say that God has given him a long life so that he could take care of his followers. So consider them in the light of what happened with prophet Mohammad who left his followers after the message was completed. If the Dai has to live for his followers, then his followers are definitely a lot of work don't you think?
6) Syedna is the first Dai al Mutlaq to travel to North Africa and retrace the historical sites of Aimmat Tahereen (SA).
huh!! He is the first one to be able to afford first class air travel and air conditioned limousines due to his inhuman practices of collecting money from his followers for his luxuries.
7) Syedna has travelled in the Concorde, the fastest jet.
So have a lot of others including the Italian Mafia.

Syedna (TUS) cruised in the Rotterdam to Bait uil Muqaddas and in the QE II to Singapore.
Again, this simply displays his lifestyle and not his spirituality. His followers might be impressed with Concordes and Cruises but most believers are not.
9) Syedna's (TUS) voice at the age of ninety plus is so clear that a computer analysis in Germany interpreted it to be the voice of a 40 year old.
Seriously? Is there an official paper that was published about this study? Or did you hear it from an Amil in a Vaez and have taken it to be the ultimate truth? I have a statue of Liberty to sell to you in New York. It resembles the Syedna if you look at it in the night without any light.
10) Syedna Mohammed Burhanuddin (TUS) is the first Dai al Mutlaq to visit Europe and America.
This only tells you that he has been looting his followers even more than the previous ones.
11) Syedna receives files and letters requesting benediction or counsel by the hundreds everyday. A file stays with Syedna for no more than 24 hours before it is answered.
Even President Barack Obama answers his mail and Dick Cheney used a machine to sign condolence letters to the families of those who died in Iraq. What this is demonstrating is idol worshipping and nothing else.
12) It was in 1389 Hijri that Syedna (TUS) initiated the tradition of ehya on the 30th of Shehre Ramadan.
Cannot comment on this as I do not know what this ehya is.
13) Syedna Mohammed Burhanuddin (TUS) built the Raudat Tahera in Mumbai over the qabr mubarak of his father. The mausoleum is the only one of its kind to have the entire Quran inscribed on its walls.
Again a waste of people's money and a place to commit shirk. I would demolish it and establish something that serves the community without the idol worshipping.
14) Syedna Mohammed Burhanuddin (TUS) was born on 20th Rabei ul Akhar which corresponds to the day of zuhoor of Imam Mehdi (SA).
Actually, I am sure a lot of other people were born on that day as there are only 354 days in the lunar calendar and millions of people born every year.
15) Syedna Mohammed Burhanuddin (TUS) memorized the Quran at the age of 21.
Kids who start early memorise the quran at the age of 13 or 14. And the Syedna cannot read the quran without a huge copy of it in front of him. Either he has forgotten it or never memorized it.
16) Syedna Mohammed Burhanuddin (TUS) built the Mahad uz Zahra, the first of its kind in the world for the study of the Quran.
I don't know where this is and what kind it is and since I haven't heard of it, then I don't think it is anything special. Schools and Colleges for Quranic study are plenty and very famous at that.
17) Syedna's audience for his community often runs into several hours as he personally listens to individuals, sometimes numbering 3000.
hmmm.... let us see, 3000 * 252 (atleast) = 756,000. That is a lot of money in any currency for a few hours.
18) Syedna (TUS) speaks several languages: Arabic, Lisan ud Dawat, Gujarati, Urdu, Hindi, and English.
My room mate in chicago used to speak 5 languages, Hindi, English, Tamil, Telugu and Malayalam. But he used to wash dishes after I finished cooking. Besides, Lisan ud Dawat is not even a language.
19) Syedna (TUS) personally conducts the annual oral examinations of the students of Al Jamea tus Saifiyah in Surat.
Again, have you verified this claim? I don't think he does. Even if he does, he is invited after getting a lot of cash.
20) During his visit to North Africa, Syedna confirmed the location of urf ud deek, literally the crest of the rooster from where Dajjal, the enemy of Imam Mansur (SA), fled.
I am not even sure what that means. Sis Fatema, can you explain this? Who was Dajjal? Was Imam Mansur following him?
21) Syedna (TUS) personally tutors his children and grand-children in religious texts for several hours at a stretch.
Can't comment on what he does in his house, but looking at his condition outside, I cannot believe he can spend that much time with his children (who are probably older than my father) and his grand children who are probably my age. Unless this was written 50 years ago.
22) "This is not the Key of the City, it is the key to our hearts." This is what the Mayor of Houston said when he presented Syedna (TUS) with the Key of Houston.

Politicians say all kinds of things, and people quote them 25 years later. I am sure no one remembers the name of that Mayor and that Mayor doesn't remember the people to whom he has handed over the keys to his heart.
23) The chief protocol officer in Sydney, when he received Syedna (TUS) said, 'I have yet to see such a powerful and pious personality.'
Don't know what a chief protocol officer is but Bohras seen to get turned on when people who have no clue about Islam talk about their Syedna like this. Realize this, THEY DON"T MEAN IT. They are simply playing "suck up" because they were paid. Has this guy ever attended any of Syedna's majlis? When he sees so much pomp and show at the airport and the abdes falling at his feet and kissing his car tire, he is bound to make a comment like that even if he wasn't paid.
24) Dr. Usman Yahya (now Mohammed Yahya) when he prayed namaaz with Syedna (TUS) at Fatemi masjid, Mumbai, said afterwards, 'today I felt like I prayed behind Rasulullah.'
Seriously guys, how much money did he have to pay to pray behind the Syedna? He better receive the same sawab!! Anyway, I have prayed once behind the Syedna probabaly 20 years ago and had no clue when the farz started and when it attended and when the maatam started. After that I decided never to run to pray behind him as I have to go home and pray again.
25) Syedna (TUS) has performed nikaah of mumineen in trains and even onboard a plane.
This just tells you the length he is willing to go to make a few extra bucks. The mumineed in trains and planes had to make arrangements because that was the only time the Syedna was available. The Syedna didn't travel to make the marriage, the couple had to travel with the Syedna so as not to disrupt his schedule.
26) Syedna (TUS) is known in Arab countries as "Azamat us Sultan" meaning the "great soveriegn".
The Arab countries you are talking about are lying. He is known as a Mushrik in those same Arab countries.
27) Syedna (TUS) is known in Kenya as "The Rain Maker."
Every guy in Africa with a feather on his head and a jhadu in his hand is a rain maker.
28) Syedna (TUS) restored the masjid of Imam Hakim (SA), Al-Jamea-ul-Anwar, in a record time of 27 months, a feat even the UNESCO hesitated undertaking.
Have you ever seen Extreme Makeover Home Edition? Beautiful homes, that defy explanation, are built in 7 days. It is simply a matter of how much money you are willing to spend. And in the case of Syedna, he has an abundant supply from his idiot abdes.
Also, when the abdes want to copy and paste from Wikipedia they might want to edit some stuff like "
.[citation needed]." out. Do they know what that means?