"I could care less" could mean anything other than "I don't care completely", including "I care passionately about this, it is the thing I care most about", thus making it meaningless. If I said "I could work less", would you assume I meant "I work almost zero hours"?

True there's ambiguity there and the sentence alone really only conveys that the topic isn't one that the stater wants to focus on any further at the moment.

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 :).

There are two ways to look at this: What the words actually communicate, and what you know them to mean. If you told an alien "I could care less", they would have very little information as to your state of caring. Therefore, the phrase fails in that respect.

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).

If on the other hand you said "I could work less," I would assume that (note the italics).