Ya I can see that. You can be empathetic but not be perceived as empathetic. it is good to develop solid enough social skills to be able to communicate empathy!
Discussion
I think empathy is the ability to vicariously experience (and anticipate?) some portion or analogue of another entity's emotions (and react in appropriate ways?).
Notice those parenthesized clauses?
I think that common parlance often makes or ignores those subordinate aspects depending on whether it suits their thesis at the moment that they're using or considering using the term.