This is not a player conflict. This is a game-mechanics problem.
I'm not sure it's possible to separate the two within the BGS, especially when considering the actions of players not deliberately aiming to cause particular BGS outcomes.
Everything Frontier does can change the BGS balance - the combat rebalance caused permanent swings to stable influence levels in hundreds of systems, the Odyssey release caused a rapid collapse in Anarchy controlling factions - not because Frontier were aiming for that outcome, but because the incentives set up caused player aggregate behaviour to change. The distorting effects of permit-offering factions have been around a very long while, but of course the desirability of particular permits can change regularly.
And of course in Elite Dangerous lore there is a conspiracy who manipulates pilots into taking actions on their behalf by manipulating incentives, so they can justify anything that way...
I don't think satisfactory answers are ever going to be practical in general - there's always going to be conflicts of interest between the plot, organised BGS groups, disorganised players just trying to play the game, etc.
In this particular case though, I think the proposed solution of making Peregrina Aristocrats a non-influence faction on their megaship is a good one:
- it allows new players to continue to receive the permit, which is good because that shouldn't be something you can stop purely by BGS operation.
- it therefore allows those players, if they choose to and can overcome CEC efforts, to push PA into expansion from their home system again. I'm all in favour of BGS operation having major consequences, but they should never be irreversible.
- it recognises the substantial efforts made by CEC to crush PA in a way more interesting than "sorry, you can't do that": I do respect that Frontier generally doesn't go for that as an answer in most systems, and therefore allows BGS events to contribute to the overall narrative
- making crushing the permit-giver back to their home system a pre-requisite both explains why it's not been done for Alioth Independents et al, but also gives player groups with a nearby permit system at least a theoretical route to success, potentially leading to interesting BGS campaigns and player-generated content in future.