I've had it happen several times. I rent small cars because I like small cars. In my experience, Thrifty and Budget usually ask for $$, but if you refuse, they relent. They typically want to downgrade me to an SUV (which I refuse to drive on principle) or PT Cruiser (the ugliest car in history) even when they have the car I want just because nobody else wants those either. I tell them to give me what I want or give me a free car, and though I've never gotten the free car, I did get a free tank of gas for accepting the downgrade from an economy car to a full-size car.

I long for a class-action lawsuit against the rental car companies to stop this fraudulent behavior, but I know there's no way they'll ever be punished. So I've gotten in the habit of reserving from multiple companies - if one won't give me the car I reserved, I can go to another. I've even reserved multiple cars with a single company (one in my name, one in my wife's) to see if that works, but it seems to have little effect.