You know, this may seem unrelated, but there's something that I do. A lot. I tend to able to sense when people are troubled or angry. Unfortunately, I usually take it personally and think they're angry at me, when most the time they don't even know me!
My friend tells me, "Beth, don't overestimate your nuisance-ability." and then laughs at me.
Another good saying: "Don't worry about what people are thinking about you, because most of the time they're not."
I do that, too. I think it's the way I was raised that gave me that mindset. I'm no spring chicken and I'm STILL fighting it. You're right that it can make you over sensitive. I hope these people take up the offers and make a better life for themselves but this they will carry.