What hellscape are you living in? I have never had anyone try to trick me like that. I'm not saying theft doesn't exist in Denmark, but it is not something I have ever considered when helping a person out.
Any tourist area with a lot of people is going to be an area with potential for pick pockets and other theft of opportunity types. Even Vatican City has a crime rate often upwards or in excess of 1.5 per resident, and that's only what is officially recorded. Most people don't bother reporting a loss when there's no chance the police can do anything about it anyway.
The vatican city, having essentially no residents, would obviously be an outlier in any statistic measured against residents.
I take your point though, but I have to wonder who in their right mind would go to times square to ask to borrow a phone. Surely you'd go somewhere less busy.