I have listened to Americans say the phrase "I could care less" and it clearly appears to be derived from the original phrase "I could not care less". The original phrase has a logical underpinning, in as much as it states that the level of care being directed to something is so small that you literally could not care less. The American version appears to be an artifact from repetition of an uncorrected error. An error that is so illogical regarding its statement and application that at some point some astute American man/woman of letters must've commented on it and so, reveal the period that its odd and illogical acceptance in to American vernacular came about.
This is not an American version. It is a sarcastic version. The problem comes from the "not" free phrase never being used in anything other than in a sarcastic way. No one ever sincerely says, "Thank you. This is important to me. I could care less." Even though logically it's positive it has a strong negative connotation. That's why some people don't even think of it as sarcasm, they learn it by rote and ignore the logic. See also, double negatives.
Once you understand the logic and sarcasm it's easy to see. If you don't then it's not.