Most people would see 'SWAT' or 'POLICE' and comply far longer than you think. Anders Brevik banked on that exact idea in order to carry out his terrorist attacks.
Hell, there was the McDonalds thing a few years ago - a store manager gets a call from what is claimed to be a cop, accusing one of her staff of stealing a purse. The staff member, an 18 year old girl, was brought into the office. The 'policeman' on the phone had the manager strip search this 18 year old, then for HOURS she was held in a back office, nude, being made to do increasingly bizarre things. It took that long for someone else to figure out this was some kind of horrific prank.
Both the manager, and the VICTIM, both said that they believed a policeman was on the phone and the manager felt she was doing what she was suposed to do. This problem is a decade old - prank callers who call managers and pretend to be cops, convincing business owners to do bizarre things for their staff.
On the phone. No badges, no uniform, just a voice on the line.
We underestimate how well programmed we are to respond to percieved authority - the white coat syndrome is very real.