Quirrell has slipped up before, when he tried to kill Bahry. Every rationalization Quirrell later gave for why it would have been stupid was absolutely correct, but I believe he did sincerely try to kill him. In the heat of the moment, in the depths of his hate, he decided to do what he felt like rather than what was smart.

Of course, this encounter with Hermione is not like his encounter with Bahry. But he is pretty agitated; he sounds agitated, anyway, and it fits, given that it took him a few hours to find the right lever to pull with Hermione. At any rate, he has no reason to be particularly careful with what he says to someone he's planning to Obliviate anyway. And given all that, I think Eliezer was not acting out of character to pick that moment as a time to throw us some scraps.