Eg, if someone is paralysed with grief and someone else comes up to give them a hug, the hugger is probably acting empathetically even though they aren't mirroring the emotion. It is more about identification and choosing an appropriate response. It is a common tactic of high empathy people to respond to negative emotions by embodying positive ones rather than mirroring the painful ones.
Managers shouldn't be making empathy conditional in the usual sense of the word, it is necessary in all settings to maintain an orderly, pleasant and respectful workplace. The article probably means something similar to but ultimately not exactly empathy. Probably sympathy, which gets used in the same paragraph. High empathy, low sympathy is par for the course for a good manager in a hard conversation.
You don't want empathy to be a blocker to telling the truth, fair enough. But one of the lessons high empathy people have to learn is that having empathy for someone and controlling how they feel are two completely different things. One is possible, the other is not. And usually there is a simple way to tell the truth that doesn't hurt anyone beyond what they do to themselves.