Yes, you're right, not low empathy. We feel empathy, WHEN we are successful in tuning into it, IF we manage to pick up the cues we need to. But, sometimes we don't whilst others might. It's difficult to measure or quantify.

Psychopaths/narcissists have a "low empathy" problem, not autists. It's almost like mis-applied empathy in a way, I have felt empathic towards animals and people when most others would not, by the same token I have felt no empathy when most other people would. So, it's difficult to pin down. But, I think it might very well be possible for an autist to "detach" from a certain situation and manipulate it, when he/she simply failed to read the cues to have empathy at THAT particular instance. He/she might be a very empathic person otherwise.

I STILL have this theory that when autistic people DO feel empathy, it is much stronger than what neurotypical people may feel. I know it cannot be proved, but I do believe it. If you simply look how certain situations or people/things have a profound impact on the autistic person, you can actually observe it. It explains well the attachment I felt to certain people and things in my life, versus the seeming ease with which other people can "move on" in life after loss or detachment from the attached object/person.