This is true prima facie, as a snapshot of "caring".

But prolonged exposition and mutual relationships (even ones kickstarted by selfish, careless objectives such as "Pay me!" or "Go to war for me!") necessarily lead to intertwining of identities. And once you consider something (or someone) a part / extension of yourself, caring follows.

In other words, given enough time and substantial interaction, the lines between "you" and "me" blur. That's just a biological (physical?) observation; cf. parasites and symbionts, nation building, product marketing, leadership…

Of course it's a scale, not a binary care / don't care. A doctor may care very little about a celebrity he knows he'll be interacting with for a year or two, max. But family doctors still exist, too.