The first part helps because it's new information to me, but the second half is not really because I am a psych major, so I know about it.
What the psychiatrist told you also goes with other negative emotions such as stress and depression in DASS (depression anxiety stress scale test).
I just don't agree because if I remember back in middle high school, a counselor took over the class for a while and explained the definition of empathy and sympathy.
It's the same thing like what you posted but simplified to make it easier to understand.
Even at that time with that they said and all to this day, it's still not the same as what Empaths can do/go through.
So if I hear people use the word 'empathy', I will go with the psychological definition and not relate it with Empaths. (people have empathy but they are not Empaths)
Different opinion...nothing wrong (I guess).