I don't think your comment even addresses what they argue. In the case of the drug addicted homeless person with mental health issues, context doesn't change that different people have different perspectives. For example, I believe that the system is imperfect, and yet it is still cruel and unjust for both the homeless person and innocent members of society who are the victims of violent crime for said homeless person to be allowed to roam free. You might believe that the risk to themselves and others is acceptable to uphold your notion of civil liberties. Neither of us are objectively right or wrong, and that is the issue with the definition of empathy above. It works for both of us. We're both empathetic, even though we want opposite outcomes.

Maybe we don't even need to change the definition of empathy. We just have to accept that it means different things to different people.