Players characters evading direct questions

[Reversefigure4]

For what it's worth, here's how the situation might have played out at my table: (cut for brevity)

An excellent summary, and pretty much how it might work at any normal table. But you're forgetting option 3T.

3T
Player: This is total bull****, GM. We should just kill all the NPCs if they won't bend over backwards for no reason.
GM: There's an answer, but I won't tell you it.
Player: This is just like <lengthy angry discourse about unrelated out-of-game incident 4 years ago>.
GM: I was right then too, and I won't change my previous reply to provide more help, even though you're telling me you're frustrated.
Player: <Throws something, curses, and walks off>
GM: See you next week! (Aside) Good thing these players are so terrible they have nowhere else to go, or I'd have no players at all.