The problem is, as MrP indicates, that spoken, colloquial, English does not necessarily follow strict grammatical rules.
What you have to listen for is the tone in which each is said.
"I could care less" said with a tone of scorn carries a particular meaning - the thing under discussion is of little importance, and that is what I am sticking to.
"I couldn't care less" said in a dismissive tone rather implies that the person actually is aware that they should care, but is determined not to admit the fact.
Student or Learner