I just edited my above comment to add the middle paragraph, before I had seen you replied to it already. I think it answers your question: not-caring can be helped along by several false beliefs, but then again caring can be helped along by several false beliefs too.
If it’s really caring as such that we care about, this seems like an easy question. People tend to care more about people when they know personal details about the person. We would therefore expect accurate knowledge to show at least some correlation with caring, unless fear or deliberately misleading knowledge came into play. (And fear should matter less under CEV, if that rule works at all.)
I just edited my above comment to add the middle paragraph, before I had seen you replied to it already. I think it answers your question: not-caring can be helped along by several false beliefs, but then again caring can be helped along by several false beliefs too.
So we should ask about the correlation?
If it’s really caring as such that we care about, this seems like an easy question. People tend to care more about people when they know personal details about the person. We would therefore expect accurate knowledge to show at least some correlation with caring, unless fear or deliberately misleading knowledge came into play. (And fear should matter less under CEV, if that rule works at all.)