Yeah... no.
I think some people have invented some "legitimacy" rules after a number of years in the game that are not coming from FDev, and are not coming from those who played the BGS from Day One. I think this starts with a fundamental misunderstanding of what PMFs are.
PMFs didn't exist at launch. They are a later invention at the request of the community (which, personally, I wish they never had accommodated) and in its initial implementation was deeply flawed (initially they literally gifted the system to the PMF). While the reaction of the community was clear: PMFs should work for their home system, I think it did create a perception that PMFs were somehow special.
They're not. They are minor factions like any other. They behave exactly the same like any other minor faction in the BGS. Getting your PMF doesn't confer ownership or executive control. There is nothing that stops anyone in the game to start to work for or against your faction.
That also means that there is no legitimate and illegitimate BGS play. All of it is still just pushing minor factions. I don't care for PP BGS, but it is just as legitimate (I just don't like it, because it is for entirely different purposes).
We are all disadvantaging new groups by playing, by establishing our various territories. A recognized PMF closes space off more completely for new PMFs than un-recognized factions pushed by players. No new PMF can be inserted into your systems, but we got four(!) inserted into our 2nd faction last round. We don't mind, but obviously, not as nice for those who got their new faction.
Related to this is the idea that somehow FD endorses PMFs to take their home system. Not quite. FD just adds them into the game with a home system. That's as far as the endorsement goes. No PMF deserves their home system like no minor faction deserves their home system. There are typically at least 5-6 home factions in the system, each have as much right to rule as the next. It all just depends on player actions.
Player groups put all kinds of self-imposed rules on themselves, and people should play how they want. Splitting BGS play in legitimate and illegitimate is a fool's errand, and while I can understand it may get you some sympathy with a section of the community, it doesn't mean anything beyond you telling other players they're not playing the game right.
Finally, the typical PMF owns no systems and no assets. Large factions like yours and ours are exceedingly exceptional in the galaxy (whether official PMFs or not). Maybe we should talk of PSFs (Player Supported Factions) rather than PMFs, as some of the biggest factions in the game aren't PMFs, but definitely Player Supported, whereas the majority of PMFs is not player supported at all.