No, I'm sorry, but you are wrong and now you're changing what my post was about. I haven't been talking about who is responsible for damage caused by the flyer of the drone. I'm talking about a hobbyist registering a drone and which person(s) must register that drone. Again, like a car, you are registering the vehicle (the drone). The dispositive point here is that every recreational drone user does not have to be registered to fly a drone. So it is not the drone user who is registered. It is the drone that is registered. The only users who must themselves be registered are those who are subject to the 107 requirements.
If you are flying a done and the registered owner is not there with you, you should probably carry a copy of their registration with you, just as, if you borrow a car, you must have a copy of that car's registration with you, even though that car you borrowed is not registered in your name.
As far as legal responsibility goes, merely registering a drone does not make you legally responsible for what happens with it. I have not seen any language that states that, and I can speak with a good degree of authority on this as I have a law degree and practiced law for many years. Again, the analogous situation is a car. If you loan your car to someone, you are not necessarily responsible for what they might do with it (depending on state law). In at least some states, your automotive insurance can be required (or, if not required, may anyway) cover a wreck the loaned-to driver causes. But that driver who borrowed and wrecked the car will also be liable. Furthermore, if you loan your car to someone who is drunk or you know to be a drunk or reckless driver, that can establish liability on your part, too. That is a matter of statutory and case law. Do some states have laws making a drone user liable for whatever damage someone they let fly it causes? I don't know. I don't know the laws of every state, of course. If you know of such laws, please cite them.
Again, you have this confused and are making unsupported presumptions. Your presumptions, were they true, would have some logic to them. But that does make them true.