I suspect that the fact that they are saying it at all, negates their "don't care" statement. If they didn't care, why even mention not caring?
Exactly, well said. That's absolutely correct and the key issue here. If you really don't care you actually wouldn't feel any need to mention it at all.
It is like many things - when they feel the need to defend themselves, they have already lost the argument.
Yes, arguments. Why and for what would you argue if you don't really care about what's been said?