The hostile bases we'll encounter in Horizons, we actually have no clue what mechanic is at work, why are they hostile? Some will be due to simple mechanics, it's a covert pirate salvage operation base, destroy it! And that's about all I've seen on the subject of hostile bases.
Hostile Factions, that's a PP thing, and if you are aligned with any PP faction, you'll be Hostile to ALL other PP factions, even your own main faction like Federation/Alliance/Empire. I was with ALD, I was hostile to all other PP Empire factions, as well as every other PP faction, I was still able to buy my Clipper over in Sirius Corp space(discount!) and went from 1st rank Fed to CPO while Hostile to all the Fed factions while doing the Hutton Orbital CG. The only NPCs that attack you in that case are PP specific NPCs, they'll have some title/group name along with their name, indicates they are a PP faction specific NPC, only ones that attack you, and they'll attack you ANYWHERE you are, even your PP faction's home system.
Starports on planets will not be hostile, planetary bases are a different critter, and starports are really what player groups would want, and therein lies the problem. You can't allow them to have a static station that will cross the modes if they can control access, and they will demand that access control, without it, they don't actually control anything and that defeats the point of controlling said station.
FD already stated, these are all static across all modes, what happens in different instances varies, but a player controlled station will exist in all modes, so any exclusion lists it ha will exist across all modes, and that's not going to work, you'll annoy the mass of the playerbase, the single players not in groups, and that's business and game design suicide.
I fully agree with the idea a planet can not and should not be owned by means of it's main starport. I however do believe having your own "inflatable base" could be a strong feature with the potential to add depth.
The latter is what I would suggest as appearing ( or not at all ) as one of the salvage operations. Pillaging a clan's inflatable base. To the solo/group it would appear out of many just another mission, and in open just be that little place you can stock modules, stock some trade goods, minerals and dock ships.
That's exactly what Op's suggestion is about: "we are given a small outpost base on some random planet."
Dismissing his idea based on the premise that we don't want player controlled factions taking over systems & planets is strictly off-topic and irrelevant to his idea.