I think many of them are true. I witnessed a case where a young lady slipped on the stairs and fell down and nobody approached her, but everybody around turned on their cell phones and called 911. So, as a simple rule, always keep to yourself.
As to the police, my experience with the US police (Washington, DC) is that they are ok as long as you act as a friendly, smiling and obedient tourist looking your way around. They initially act very aggressively, maybe rude and take lots of precautions with you as though you're a dangerous mafia, so fight your natural instinct to get back to them with the same attitude and they'll do nothing to you. Have a nice travel!