Some people have ultimate confidence in their social judgements and the true sign of empathy is a kind of meta-empathy that allows you to consider truly alternative understandings of the world i.e. empathy for empathy.
One explanation I have for this is that precisely because empathy is a more rare experience for them, it becomes a more remarkable one, perhaps even overwhelming at times. This leads them to believe that they experience it more than or more intensely than others, when on the contrary the rest of the world is simply more habituated to it and integrate it more gracefully in their ordinary experience.
The other interpretation is that it requires certain level of narcissism or egotism to describe oneself in such flattering terms.
Or ultimately, as the Spanish proverb says: dime de que presumes y te diré de que careces.
Probably some degree of all of this is true in most cases.
An introspective, empathetic, thoughtful person might still accidentally say something that an external observer might perceive as having been said without thought or consideration to the feelings of others.
The above is not meant to be contradictory to your point, just a consideration to the general faults all humans hold.