I am glad that you value words, language, and meaning. So do I.
But people who say "I could care less" are usually not mistaken. They know full well what they mean, and that the phrase seems to say the opposite of its literal meaning.
It's a great example of irony and sarcasm, both of which have a rich history in English, and probably in most languages.
Pinker has a fine discussion of the phrase in the book I mentioned. I can't do it justice here, but consider how the phrase is spoken. I will use italics to indicate emphasis:
I could care less.
Try saying that out loud a few times with emphasis on the italicized words. You may start to hear the ironic and sarcastic intent.
English would be a much poorer language if we could only use words and phrases in their most literal meaning.
Also consider the context. "I could care less" is used in casual speech, where it's perfectly OK to play with the language and have fun with it.
That is quite different from, say, a manual on how to operate a piece of machinery, or any other kind of technical documentation. There of course you want to be as clear, explicit, and unambiguous as possible.
But I wouldn't judge someone's ability to write a clear technical manual based on their enjoyment of irony in more casual speech or writing.