Nah, you can care about someones utility function instrumentally. In fact I think that's the way most people care about it most of the time, and have no reliable evidence to suggest otherwise.
I meant 'caring' as in direct influence of their utility on your utility (or, at least, the perception of their utility on your utility), conditionally independent of what their utility results in. If you take 'care' to simply mean 'caring about the outcomes' then yes you're right. Saying that all people are that way seems quite a strong statement, on par with declaring all humans to be psychopaths.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.