My suspicion is that Boise State had a very thin knowledge of his issues with women and that almost the entirety of his issues were surrounding the depression and behavioral problems that manifested in the form of general violence and aggressiveness. He probably got in a fight with other players or perhaps the coaches or other students -- I don't know, but I suspect that's what got him kicked off the team.
Peterson then advised Briles of these behavioral issues, and Briles saw the potential to pick up a talented guy while assuming he could control him enough to limit the problems he would cause. The real problem here is Briles turning Baylor into a 'second chance' program willing to take risks on troubled athletes. Sometimes that works out in a positive way for everyone but sometimes it doesn't -- this being a case of the latter.
But do I think Briles would have run such a risk to the program by bringing in a guy he thought beats up and rapes women? Uh, no. And there's no evidence to suggest that he did.