You’re almost completely right. You can only receive the amount realized from the car–if the charity sells it. If you can find a charity that can actually USE the car, you are still entitled to fair market value on your tax return. And most cars that are sold at a typical auction are sold for a lot less than their fair market value–if they are sold for much at all.
I donated an old Camaro (you could almost R & R the exhaust pipes from inside the car) in 1992 to Volunteers of America and received a credit of $3300 (which I couldn’t take, since I didn’t itemize). I have attended some of their auctions since and seen a lot of cars that did not make their minimum bid of $100. These cars are probably sold to a local junkyard–sorry, automotive recycling facility–for a lot less than $100, which would make the ultimate tax credit a lot less than $100.