Almost every every person I've met that describes themselves as empath tends to rank rather low on empathy, under my own judgement at least.

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.