I'm certain that eventually you'll discover that, as a past winner, Woods has a lifetime invitation to play in the Masters. That's only one of the many benefits awarded to a winner.
Until 1999, players winning a PGA event were invited to play in The Masters the following year. They changed that qualifier, then re-instated it for the 2008 tournament. It's a private club completely independent to the PGA.
If the decided to rescind the standing invitation (which I doubt), it's unlikely you'd hear any outcry from the field. Sports writers (other than CBS), sure.....but not the tour players.