What if the coach told you, "No. I didn't mean right now. I meant at the 3:14 mark of the third quarter in the game we have a week from Tuesday. Wasn't it obvious? DUH!"
In that case, I'd call an inadvertent whistle and cancel the timeout. Then I'd toss the coach across two zip codes.
My point is if the coach acts in a "standard timeout request" mode - grant it if he or she is entitled to it at that time.