The problem is she didn't win the slot based on merit. She won it based on affirmative action, hitting from the short tees, because she is a woman. She's taking somebody else's hard earned position. Thats the problem in a nutshell.
And as far as everyone playing from the same tees in the "Full tournament", that is another reason this women shouldnt play in the PGA event. She did NOT play from the same tees as everyone in the event she won. So, at best, its an illegitimate win and clearly not one worthy of gaining an exemption into a PGA Tour event.