It's "I could not care less" not "I could care less". If you could care less, then that means you care. If you can't care less, then that means you are all out of fucks to give.
I've read somewhere that English teachers and grammarians agree that "I couldn't care less" is the correct one, and it makes more sense to me too.
Although, I can see how "I could care less" could mean that: you care so little that if you wanted you could care even less, but you don't care enough to do that.