McGonagall is savvy enough to know that the current defense professor is at fault for something like this; Quirrell pushed his luck in manipulating her into taking the actions she did, including providing him a single point of false-memory charm to an alibi for whatever he needs to do (including stealing a time-turner, meeting his future self, confirming that everything appears to will have gone well, and then going back to set up the scenario in the first place).

ETA: And even if it wasn't Malfoy & co, it is believable that they would think it was one of them.