To a mathematician, some things are far more important than mere money. Accepting tribute money from an organisation you believed to be fundamentally corrupt would be to become one of the very people you despise.
I know, my PhD is in pure mathematics - I've seen up-close that mathematicians can be an odd bunch ;)
Using the money to fund some kind of an alternative to the organisation he believes is corrupt, surely wouldn't make him corrupt though, just to take one example?
Had he just accepted the prize, there would probably be little mention of it in the main stream media.
I couldn't resist thinking about this a bit more. Something comparable would be firefox's double-page New York Times ad, which apparently cost about $200k (http://weblogs.mozillazine.org/asa/archives/007103.html) and certainly reached a lot of non-mathematicians.
Even though Perelman's action has generated quite a bit of press attention, my gut feeling is he could have paid for even more attention if he chose to use the prize money to raise awareness directly.
That said, if he really wanted to get maximum exposure, he could continue to ignore the prize for almost a year, but accept it at the last minute and then spend it all on ads telling the world how corrupt academic mathematics is ;)
I'd think generating interest from something minute would be harder than from something a lot of people have at least heard of.