You are assuming most people pay as much attention as you do. Most people donate to the charity they see on TV the most. They don't give a shit about said charity's efficiency, they just want to say, "Oh, I got this pretty pink ribbon, see how great I am!"
They probably assume that if a charity wasn't making good use of the money, government would do something about it. A poor mentality too often encouraged.
Oh come on man, you are really stretching here. Most of them aren't assuming anything at all. They don't think about it. They did their good, leave them alone is the mentality.
It's human nature to seek rewards for what we perceive to be good deeds. If anybody is taking advantage of these people, it's the charities handing out the goddamn ribbons and throwing their ads on candy bars and shit (where probably a whole 5 cents will go to the charity), or talking about how a portion of proceeds for that $600 dress goes to charity (and almost certainly as relatively small a portion). And they're not exploiting sheep. People are not sheep. People are glorified, tribal monkeys. They're exploiting our monkey tendencies to seek out rewards and get mad when we are given a slice of cucumber for our good job rather than a grape.