It is not a technicality.
The fact that the Masters is one of the four majors is not a PGA concept. Two of the other majors, the US Open and The Open (the British Open), are not PGA events (the US Open is a USGA event).
None of these events are on the PGA tournament schedule.
There are many weeks in which there are no PGA events. It simply makes economic sense, since the best players in the world will be at the Masters, and no other event (PGA or otherwise) could compete for coverage necessary to justify the economics.
It is not a de facto event for the PGA - it predates the PGA. The PGA has absolutely no influence over how the event is held.
While lawyers could argue that it is a PGA event, I can hardly see how they could make the case. For crying out loud, they allow non-PGA members to compete in it! Show me any other PGA event that does that, and I’ll reconsider your point.