I've had plenty of face-to-face conversations with my boss demanding an answer to an immediately problem that basically ended with me saying, "I need to look into this," repeatedly until the conversation ended and I could actually work on it.

Ugh. I have to go through this all the time. Boss asks for estimates for things I haven't looked into. I tell him I don't know. He pesters me for a guess, which I refuse. Round and round we go...