My previous post on this thread notwithstanding, I have never been turned down when asking to take a picture. I am polite (hard to believe, I know), friendly and non-threatening. I was rebuffed once by a night watchman, when I had actually been given permission by the owners of the facility. The watchman told me he didn't know if I was a spy, or perhaps a terrorist, who wanted to sabotage the facility. The next week I told his boss about the conversation and was told to just come back again. I ended up getting the shots I wanted and gave copies to both the owner and the night watchman. Everyone was pleased.
One thing I have found to be very effective is reflective listening (I know, even harder to believe coming from me). Try using "Gee, it sounds like you are really......" and then prepare to get a long story by way of an explanation. It does help a lot and you may find out a great deal about someone's life and some things of value to go along with the picture you will get. It works for me.