Duncan, the problem is that Urban Dictionary is like Wikipedia: its readers make all the contributions, including content. The Home Page makes this clear, right near the top, where it says, "Urban Dictionary is written by you."
This leads to some interesting definitions. For example, here is how Urban Dictionary defines "socialist:"
"Taking from the achievers and giving to lazy people. Keeping the populace under the government's thumb."
And here is how Urban Dictionary defines itself (under urban dictionary dot com):
"A website that lists the meanings for modern day terms as defined by every-day people. Unfortunately, quite a few of these people are unintelligible, narrow-minded and/or foolish. Because of this fact, one who wishes to find an accurate definition of a term they’ve heard is left with the problem of sorting through all of their nonsensical garbage before they can find an accurate piece of information."
Definitions in Urban Dictionary are no more authoritative than the persons who happen to list them. I don't believe you have cited an authoritative source.
However I have given you 3 well-established dictionary sources that say you are 100%, flat-out wrong. This includes Merriam-Webster Dictionary. Even Oxford Dictionary lists "I could care less," with the same meaning as the one you prefer.
I get that you don't like the expression. That it offends your sense of logic. But that does not make you the arbiter of idioms. They are by their nature more democratic than that. Many millions of people use this particular idiom, including highly-educated people. It is listed in one authoritative dictionary after another.
ETA: here is how Urban Dictionary's founder, Aaron Peckham, describes it: "In some ways, Urban Dictionary is the opposite of a regular dictionary — the definitions are opinionated, not researched, and sometimes even misspelled."