I wasn't aware of that.... so I just checked, and yes... its barometric. I wasn't breathing on it.... honest.
Incidentally, back in the early days of GPS... about 24 years ago, IIRC, I had my height measured by GPS. It was pretty damn accurate too, but it took a while. I was doing some work for the then Land Information Centre in NSW and they were doing some displays of emerging technology.... laptops with maps that moved.... revolutionary stuff. They had the access to the full military spec setup, so, with a bit of computing power, they got things very accurate.
Back in those days they were doing some trial mapping up where you are too... using ultralight aircraft.