What if you had told it again that you don't think that's right? Would it have stuck to it's guns and went "oh, no, I am right here" or would it have backed down and said "Oh, silly me, you're right, here's the real dosage!" and give you again something wrong?

I do agree that to get the full usage out of an LLM you should have some familiarity with what you're asking about. If you didn't already have a sense of what a dosage is already, why wouldn't 100mcg be the right one?