People really say this ("I could care less") to express that they do not care at all. I've seen it happen here on this site. Calling out the sheer absurdity of it, even in a respectful way, is not universally well-received. Unfortunately, I could care less about this, as it sounds very grating to me.

I try to remember that I ain't got no problem with other "illogical" uses of negation and could this one in a similar light, but it's more easily said than done.