That's quite an interesting subject. I have indeed met many people who fall under this umbrella, and consider myself to be one of them, in fact. Depends on the situation of course, and the motives on the person trying to give the money, in your example. But the money thing might just be the most obvious example to give. It gets much more subtle in life. There are people who are unable to ask for help, nor receive help of any kind, even when offered freely. There are people who would rather bleed out on the street than "cause a fuss" by asking someone to call an ambulance or something similar. It's a weird thing, this feeling of unworthiness, or sometimes, of pride and/or notion that you have to be able to provide for yourself, or else you are cheating in life.

We are a funny species, I'll tell you that.