Is empathy different, in those already provably lacking it? Do we have confirmed cases where empathy was provably instilled in someone who we know had none?
My two cents
* Empathy is not a binary thing that is there, or not there, or instilled to being there.
It is a gliding scale.
Similarity of level of empathy with other people more convenient for your comfort bubble
Diversity of empathy in a group in general more effective for the performance of a group
(value of diversity depending on situation/challenges faced by the group. In low needed change situations the whole group can go in equal empathy comfort bubble. Until change disaster strikes: too much empathy in a group can be quite suffocating and hinder out of the box thinking for needed solutions or simple real progress)
* Lack of empathy can have so many reasons.
Is it a lack of perception (by your mirror cells etc) from gene damage, or more extreme natural diversity ?
Is it the opposite: was your empathy too big and you got overwhelmed by outside emotions and you had to shut off drastically ?
Did you have a "normal" level of empathy and pschychological traumatical events happened. Roadblocks so to say ?
* There is emotional empathy, cognitive empathy and somewhere close compassion. What do we talk about ?
* Is your brain behind the mirror cells, or socially wired differently (going direction A-spectrum) ?
If you are wired in such a way that you feel comfortable with very defined fields of knowledge and interactions, and not feel comfortable with the more opaque and ambiguous social interactions, do seldom understand certain kinds of jokes.
Do you prefer "down to earth" situations where you can act or not, and switch off from hypothetical situations, philosophying ?
Do you prefer a pure technical job, with pure technical hobbies, similar discussion topics for the birthday parties, and for the rest your peace of mind with your sports paper and watching TV ?
Is that lack of empathy ?
On your question of confirmed cases.
I saw quite some HR assessments in my life (not the software apps, but real stuff with roleplay tests and all), and empathy was one of the things measured AND part of the evaluation discussion how to adress or improve if needed. Nothing out of the ordinary.
All in all: I think empathy is foremost an evolutionary based diversity increasing social characteristic on a gliding scale which you can and do change in practice during your life adapting to the situations at hand.
Sometimes trainings or help is needed. Sometimes that does not deliver much (and you use that as from HR angle to make clear to someone he lacks (proven) the chracteristics for a certain promotion)
Some have (too) little or little drive for it
Some have more
or even too much and annoy others with their hype on it, talking those others into guilt to get more of it, as well as other negatives
Here a nice article about some negative side effect mechanisms on empathy:
https://www.fs.blog/2017/12/against-empathy/