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.
Your explanation is a retcon.
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.
That rephrasing hypothesis is the best I've seen yet, but still not especially persuasive.
"I could care less" can mean "I could (stand to) care less".
As in, "The amount I could care about this is zero because it's so irrelevant, but in responding to this discussion or otherwise engaging the topic, I have exhibited a bit of care, albeit undue."
For fun, I sometimes like to propose this to anyone who brings it up, but I could care less whether people say "could" or "couldn't". :)
Edit: Hah! neltnerb gets me :)
Generally however, I think there's some assumption or perhaps prior demonstration that implies a lack of care to start.
It's tough to describe. "I could care less what you do with your money" may come with a long understood history that not much care was given to this topic the past (i.e. we haven't discussed it before), and if we are now arguing about it because because some prior discussion escalated, I am indicating that I preferred the status quo with that statement (albeit in a way that probably doesn't defuse tensions in this particular example :).
If, on the other hand, you treat it as a nonsensical synonym for "I don't care", then the phrase would well have been "gooble gooble goo" and it would make no difference, since everyone knows what you mean when you say it.
I find arguing its correctness moot because there's no way to spin the sentence to be correct. At most, you can say "well, you got the point", and that's the end of it, at least when you're dealing with a descriptivist (which you aren't, in this case).
But apparently the use of the word "jive" to mean "talking nonsense" is the older, original usage, and the type of music/dance is named after the term, rather than the other way around. TIL.
The earlier musical dance/reference is the really just the Johnny Otis song which is actually just a Bo Diddley rip-off:
You want "jibes" here. Jive means to talk nonsense:
https://www.grammarbook.com/homonyms/jibe-jive.asp