Where does one draw the line a very thin line for that matter. My kids (now adults) were raised on both sides of the Atlantic, and have travelled both alone and with me extensively. Very street wise. Have taken the bus or walked to school alone... have gone out alone, with their friends, since they were 14. My daughter developed ways of distinguishing legit taxis, in Paris they aren't uniformed. learnt to take a down the license on the meter, etc etc. There were some incidences of fake taxis standing outside clubs and taking mainly tourist ladies out and a few have not been seen again.
And we live in a very "safe" area of Paris This past New Year, while going out with her friends just really around the corner from the house, she was accosted by a drunk, he pulled her long hair tried to throw her down the ground and kiss her, her friend and my daughter tried in vain to kick him push him off her, all the while screaming for help. Lots of people walking by a police car passed by and NO ONE, NO ONE stopped and did anything. One person only came and helped them by pushing the man off her. Only one person. And I live just next to the tower where everyone and their dog goes.
It only takes ONE incident for you, as a parent to have nightmares that you couldn't protect your child.. She didn't go out for a long time and even now is very careful.