To be fair, that does sound like it could be a scam. Also, presumably all the police would have told you is that you should go to the nearest police station.

Once, after withdrawing money from an ATM, two guys came up to me with a 5 euro note. They told me I had dropped it and wanted me to take out my wallet. Supposedly so I could verify that I 'indeed' lost money.

Another time someone came up with some sob story and asked me if he could use my phone, or failing that, if I could make a call for him. I forget the details except that I did have to fight him off later.

These events happened in two different countries, and I have more stories like this.