I agree. It also made me think what silly words psychologists use - like cognitive and empathy.
Why not say 'understand what the person is feeling' or, alternatively 'feel what the person is feeling'. And how do you 'measure' either of those? Search me. And what sense does it make to take an average when you have done the measuring? If a student starts to behave as if they know better than the patient what their symptoms are (is that pseudo-empathy?) it is time to take them down a peg - that is the way I used to look at it.
This gets into a discussion on the evolution of language because the words sympathy and empathy do have distinctly different meanings even though they are used interchangeably today. The prefix 'sym' means 'with' (think symphony) while the prefix 'em' means 'into' (think embed). But culturally the word sympathy is associated with bereavement so many healthcare professionals avoid using it entirely and opt to use the word empathy instead (even though what they really are doing is sympathizing, not empathizing).
I once heard someone describe the difference between the two words this way:
A person has fallen down a well. An empathic person is down in the well with them. A sympathetic person is at the top of the well lowering down a rope.
There was a brief span of time when scientists thought mirror neurons were the key to how empathy works, but I think they've backed off of that idea somewhat.
The cognitive vs affective empathy is interesting to me because I generally haven't got the foggiest idea why someone feels the way they do. I might get the sense that a person is angry but I'll never know why unless they tell me.