One thing that I think McDermott has going for him is that he does appear to admit his mistakes. I do think leaving Peterman in there long enough to throw 5 INTs was rather stubborn, but like others have said, I don't see how you could start Peterman after that showing and not have the entire locker room mail it in. If they are trying to mimic the "Do your job" process that they have over in NE, it will not bode well with players if they contradict themselves by starting a guy that doesn't give the team the best chance to win.
Maybe not, but he most likely would've kept it close enough to have a shot at the end.