Most people would so not sure what is your point. The problem we now have is that in some areas the person in the river would rob you the minute you got him out. Or his mates waiting behind the tree would. Or of course the other problem of some feminist bawling you out because you dared hold the door open. (And yes it does happen I had it happen to me three time in that toilet called London)
So, you would ignore someone you thought was in danger and walk on past? That appears to what your implying from your personal point of view, especially in London.
Well if you read my post I have been belittled three times by feminists. Does that rather not imply that I have not given up hope and would go to someones assistance?
the idea that humans are in any way less emphatic in a situation where one may need help is one that is based off of negative news reports and generally the idea that humans are sinister. We're not, we're usually happy to help.
People aren't given enough credit. I live near a boys school so the local shop often full of young men. They always hold a door open for me and any other person.