Think of "I could go out less", "I could eat less", "I could spend less", etc. All these phrases clearly imply that you're overdoing it now and need to stop. "I could care less", as used, means the opposite, that they don't care almost at all.
Your explanation is a retcon.
... that was the joke. But I agree jokes are better when they're explained (not kidding).
Of course, if enough people start saying "I could care less" I guess they get to decide what it means. Living languages are literally awesome.
Of course, it's probably more literally true that they could care less, after all, they care enough to post about it on the internet. They probably don't do that for... um... articles about the 1984 Honda Accord after all?
Oh English.