According to Rich Cimini's twitter:

Gary Myers from Daily News: Giants won secret coin toss today. They get first game in new stadium, not Jets.

Secret coin toss, huh?  I guess there's no way to verify that it actually occurred, right?  The Jets released the story last week regarding this coin toss fearing that the league was leaning towards choosing the Giants.  The NFL denied that they agreed to a coin toss and said Commissioner Roger Goodell will decide.  However, the Jets were adamant that they were told there would be a coin toss and wanted it done in public.

Jets owner Woody Johnson, without whose money the stadium wouldn't exist, is none too pleased:

A source says Woody Johnson is "outraged" by coin toss -- not because he lost, but because there was no team rep present.

I think it's kind of fishy that after denying it, there apparently was a coin toss after all.  But then it was done in secret, and the Giants won anyway.