I don’t hand over my ID just because a cop has misconceptions. IF this is the way it happened, then I would refuse, as would any husband I would marry.
“thinking” something might be wrong is not proof of illegal activity, sorry.
If a cop is responding to a complaint or call, I want to allow him to get on his way. I would think nothing about identifying myself in any casual way requested so that the cop can locate whatever or whomever he is looking for in a case like this. Now, if my wife did not have her ID or the cop was overly zealous, that is a different story. We are not in the land of “papers please.”