Illogical English #16

Only one of these is illogical, because it’s actually wrong. Which one is it?
“I could care less about which team wins the match.”
“I couldn’t care less about which team wins the match.”

Well, the former is meaningless, and the latter is correct. However, the former is the one I hear almost always from Americans, and the latter is British. Of course, American English isn’t always incorrect, and British isn’t always correct; but in this case it definitely is that way.
Here is a video of British comedy actor John Cleese ranting about it: