Even if GPS is more accurate, this is irrelevant. There are numerous standards that can be used to define altitude. Geopotential (GPS, very long ruler, being on top of a surveyed mountain...), pressure, temperature.
Everybody else uses pressure, so the airliners in the CAS just above you are setting altitude by reference to a pressure datum.
If that datum is causing them to be lower than would be "correct" by reference to a geopotential datum, then the arrogant PPL who thinks that his GPS is "more accurate" could well be inside what the airliner pilot believes to be his airspace.
The good news is that in all likelihood, only the PPL and his passengers will get killed by this piece of stupidity, or better it'll just result in a diversion, delay, several thousands pounds of extra costs, and removal of the PPL's licence - but since there's a risk that he might take 300 airliner passengers and crew with him, on the whole I think that he should be strongly encouraged to stick to using the pressure altimeter required by law to be fitted to his aeroplane.
G