...and this did happen, because it happened to me, back in the 90's:
I was contracted to window dress a duty free outlet.
A few people interupted me ' can you tell me where etc.. ' Fine, it goes with the job, people think I am staff, I help if I can. A couple of men my age were very chatty, thought nothing of it. I was in again two days later.
The manager told me that the police had been in asking for me, and had requested my name and address. He was only able to give them my phone number and name.
The manager was very cagey about arranging the next contract with me, and in fact never did. I kept getting the side eye from the staff.
I was totally bemused, and a little worried, then that weekend I had a phone call - the guy explained who he was - one of the chatty men, and asked me out.
He had left the area he was suposed to be working, driven down to the outlet, used his ID to get through customs etc and to gain information about me, which he then used to ask me out.
Aren't our police wonderful. So resourceful.