I realize this is largely a lost battle but strictly speaking "disinterested" means no interest in the sense of "conflict of interest." A disinterested party has no "interest" in one outcome over another and can therefore be trusted to be impartial in the matter. "Uninterested" means what you wrote, they are not interested in something in the more everyday sense of the word. Not everyone thinks it matters but the two words do have distinct meanings, and in some situations (like in conversations about values, politics, etc) it is actually worthwhile to be precise so that one does not inadvertently mislead the reader.

Merriam Webster agrees with you for word sense 1a, but with me for word sense 1b. So you win and I agree that uninterested is a better choice here.