"I could care less" is sarcasm that has fossilized into idiom. Notice how it has a different intonation than you would expect from a simple declarative statement.
I think it's more likely that people parrot the sounds without thinking of the words and/or the meaning. Compare to "for all intensive purposes", for example.
I agree with your observation of that common mechanism for mangling English, though. The mis-quote you mention is particularly embarrassing to behold.
As others have pointed out: language is meant to be understood. It would be enough to always take the meaning from a speaker, except if we do that chronically, we begin to lose words. Which will make communication more difficult when you need those specialized meanings.
Bother.
As if I could care less.
Words that have opposite meanings depending on context, intonation, and tradition aren't that uncommon -- even single words, such as contronyms.
Writers, remember: you can't put too much effort into precise language.