[Objection #1: According to the interview, Gregory Perelman bristled at being addressed as "Grisha" by the media (Gregory/Grisha being similar to Robert/Robbie in familiarity). This could not possibly be true because he signed his own emails as "Grisha".]
This is a pretty big stretch. The Russian language defines 3 tiers of familiarity/address: a nickname for family/friends, a full first name for acquaintances of the same age, and a full first + patronymic name for everyone else. (This is similar to a French person being offended by an overly familiar "Tu" when a "Vous" is appropriate). Moreover, it is not uncommon anywhere to use a nickname in correspondence with friends and colleagues and a full name in more formal situations.
The forum discussion - your second link - is nothing more than a reference to Richard Feynman's auto biographical anecdote about the Nobel prize, followed by a bit of general bitching about journalists. One poster casts doubt on how Perelman and the interviewer connected (seems perfectly plausible to me that a Russian-Israeli journalist would connect to a Russian-Jewish scientist through his mom, whom he lives with, via the St. Petersburg jewish community). It really doesn't prove or even suggest anything of importance.
As far the claim that Russian bloggers couldn't track down the person who interviewed Perelman, well, I just spent a minute on google and found this: http://cursorinfo.co.il/news/novosti/2011/04/28/zatwornil/. Apparently, the Israeli paper was able to find the interviewer... not particularly surprising given that he had moved to Israel in the 90's.