Personally, I do not beleive the Tammet claim, but the site is well put together, and in some points, he makes a very convincing case.
I guess it depends on your view on the Romanov's story, and death too. I don't think Alexei cuold have survived, but your view could be totally different.
Whether we think he was Alexei or not, he IS a part of their story because there were many beleivers and he was a quite popular claiment.
-Dana