The people who process these requests, particularly at the large companies that possess such data, are typically dedicated to the task and possess the specialized knowledge needed to do so. They have often developed significant relationships with the law enforcement community.
Do you know them?
Do you have a connection that you could entrust with giving you a positive or negative answer as to whether the armed man with no sense of humor in the cop uniform outside is the real deal?
I don't. Hell, even if I had a lawyer on hand, I doubt the lawyer would go "hold up.. checking the registries, yup it's legit"; rather they'd tell you to cooperate then maybe challenge outcomes down the road when the paperwork catches up.
For most, the answer is they take it on faith anyone usurping that authority would have such a shit ton of bricks dropped on them, no one would be stupid enough to do it. Obviously, that logic is showing it's age.
Frankly, if I were the courts/LE and found out this was going on, there'd be a new Public Enemy #1. Trust is too important.