Even worse: They’re paid to not care.

When conducting scientific research, I'd think "not caring" is a desirable trait. You don't want anyone's personal feelings to get in the way of reporting accurate information.

I think this is just being pedantic. You have to care about something to formulate and test a hypothesis. You have to care about what the data say to bother gathering them and collating them into some report in the first place. "To care" can be "to be curious about something" or "to have an interest in something", not just "to be concerned about something."

No, you have to be interested in something. Caring implies that you have an emotional desire for the hypothesis to be either true or false and that leads to bias. Scientific interest drives motivation.