Phantom, are you saying that, if 7 people come up to you and start giving you orders, the first thing you will think of is "Oh, they are undercover cops.". No. You will think "I'm getting robbed. / Potentially raped / Maybe just harassed" The badge is irrelevant, no way for me to know its not fake.
Probably would have turned out differently if only 1 or 2 of the cops went to check things out.
I think the fact that the felony charges against the girls were dropped tells you everything you need to know.