Wouldn't that kind of be like blacking out your license plate on your car? The visible number is a requirement. Asking to come in your house would be like asking to see your video. I would probably ask for a warrant at that point. It would depend on if where I was flying gave him,..You got it,...reasonable suspicion.
There is no requirement from the FAA that your registration number be viable. It has to be on the drone that it's easy enough to location. This means it can be in the battery compartment which would require that the battery be (easily) removed. These are not tail numbers. You are also required to have that printed paper on your person from the FAA website showing your contact information and registration number.
Its possible that someone reported the OP. If that was the case I'd say the officer had a legal right to demand proof of registration (as a complaint is being investigated). But as it is, it seems like the offer simply asked for this info and would have given the OP the right to refuse. That does not require a complaint or the suspicion of a crime.