I think it's more subtle than that. Let's clarify a few things:
Types of empathy
Being around people who feel a certain way, you'll feel a certain way.
You try to imagine yourself in the other person's situation, then ask yourself what you would feel.
Some situations you cannot imagine yourself in. For instance, as a man, there are a lot of woman-specific situations I'll never find myself in. Thus, I can't really ever empathize with how they feel. Women will say "oh, you can't undestand". Indeed, I can't. So, what do you expect me to do? Pretend I can? Or accept at face value whatever capricious, random and frivolous whim you feel?
- Empathy, perceiving the information of other people's feelings.
- Your personal value system.
- 1 filtered by 2 leading to your actions.
If you have no personal value system and strong empathy, you'll be an emotional sponge, a second-hander, irrational, letting other people's emotions dictate your life.
If you have no personal value system and weak empathy, you'll be a psychopath.
Even autism is being redefined as lack of empathy filters, not lack of empathy.
Inner game is all about being able to perceive what others feel, and filter it through your own value system, whether we're talking about rational analytical empathy or instinctive subconscious emotional response. Instead of merely mirroring other people's emotions, this will actually allow you to analyze them, and, should you choose to do so, offer them valuable advice, helping them reframing their own issues.