Empathy, in this context, means to me that I care about the problem of the person I am supposed to help, which increases my motivation to actually help them.

Saying I care and actually caring are not the same. When I call a hotline with a problem and am stuck in a loop telling me how important my call is to them, it tells me they don't care at all.

At least that how I understand the comment, and since I also wear a helpdesk-monkey-hat at work, it is how I try to deal with our users.