No, you're missing my point. I'm not speaking purely, or even primarily, of legalities. I'm questioning whether the cop may have played a role in an unnecessary escalation of hostilities with the attitude he displayed toward AD or his choice of language or the tone of voice he used. Again, we don't know that the cop was in uniform or that AD had any idea he was a cop, and we certainly don't know how the cop handled the matter.
And I'm questioning a system that (if you're correct about it) allows a policeman to retain all his privileges and powers as a cop even when he is employed by a private citizen. That's a screwy setup, affording police powers (and the arrogance that sometimes accompanies them, unfortunately) to someone who is being paid to value and protect one person's rights and property over all others.
As far as I'm concerned, those cops were bouncers -- nothing more and nothing less. When you have the power of arrest at your disposal -- not to mention two of your cop buddies as backups -- that's a perfect setting for the abuse of power. A cop should a cop when he's on the city clock. When he's on someone else's time clock, he should be considered a private citizen and be bound by the same rules that apply to those private citizens. Had that been the case -- had he not had the power of arrest -- he'd likely have been a bit more patient in dealing with a customer who wasn't leaving as fast as he'd have liked, and no one would have been inconvenienced, hurt, or arrested.
Bouncers in bars across the country wait out slow-to-depart patrons on a nightly basis without starting fights or calling the cops, and an off-duty policeman should be able to manage the same feat. If he can't, he's not suited to the job of bouncer (and possibly not to being a policeman).