Human error is a consequence of being human - only humans can truly make such errors, and to do so requires that the entity committing the error is human.
Ergo, pilot error must be a consequence of being a pilot.
Not at all: 'pilot error' is a human error commited by a pilot. It is a consequence of being human, and it is commited in one's capacity of being a pilot.
Pilot errors won't go away just because we call them something else, and I must say I have never agreed with the notion that they take on a totally different meaning simply by calling them "human" rather than "pilot"... Who was unaware that pilots are human? If pilots are human, how could "pilot error" mean something else than "human error"?
25 years ago, the distinction you are trying to make might have made sense... But today, I think it is quite obvious that when someone with an aviation safety interest say "pilot error", they mean "human error commited by a pilot".