Earlier quoted context omitted.
FWIW Professional Linguists think it's perfectly fine to say "I could care less" and that people who peeve about it are just pointless peevers who don't understand how language works.
That's not the point: "I could care less" is grammatically correct, but the meaning is not what was intended. If I had a cup and wanted to tell you there's no more beer in the cup, I wouldn't say "there's beer in the cup", even though the sentence "there's beer in the cup" would be accepted by professional linguists.
The intended meaning is obvious. There's plenty of colloquial phrases which say one thing but mean another: "I could murder him", for example, doesn't literally mean that. That is how language works.
And, if you saying "there's beer in the cup" was understood by everyone as meaning "there's no more beer in the cup", professional linguists and dictionaries would be A-OK with that interpretation.