The vast majority of yes/no questions you're likely to face won't support 5% intervals. You're just not going to get enough data to have any idea whether the "true" calibration is what actually happens for that small selection of questions.

That said, I agree there's an analytic flaw if you can change true to false on no additional data (kind of: you noticed salience of something you'd previously ignored, which may count as evidence depending on how you arrived at your prior) and only reduce confidence a tiny amount.

One suggestion that may help: don't separate your answer from your confidence confidence, just calculate a probability. Not "true, 60% confidence" (implying 40% unknown, I think, not 40% false), but "80% likely to be true". It really makes updates easier to calculate and understand.