Good points, you're right. I think the reason I identified the second example as not caring, despite having "thought" about it, is because "caring" might only qualify as caring if more than one person recognizes it as such. You can't really care about someone unless they exist, can you?

It requires two people at the least, if we are on the subject of empathy.
What I mean is; is it caring if you think about the other person, but the other person does not know of it?