"What's been going on?" she said. "There's all sorts of rumors. There were people saying you'd run off to fight Bellatrix Black, there were people saying you'd run off to join Bellatrix Black -" and those rumors had said that Hermione had just made up the thing about the phoenix, and she'd yelled that the whole Ravenclaw common room had seen it, so then the next rumor had claimed she'd made up that part too, which was stupidity of such an inconceivable level that it left her completely flabbergasted.

"I can't talk about it," Harry said in a bare whisper. "Can't talk about a lot of it. I wish I could tell you everything," his voice wavered, "but I can't... I guess, if it helps or anything, I'm not going to lunch with Professor Quirrell any more..."

Yes, he is. A promise to lie can be broken or kept with equal loss of honor.

Nothing about the break-in. He can talk about other matters, presumably including Quirrel's answer to his "Why am I not like other children", which did make him trust Quirrel less and is a plausible topic of conversation either way.