I think this is the most important bit that's left to figure out because it's quite important. In my vision, factions should either harass you for "pirating" their blueprints (unless you legitimately acquired bp's from said faction somehow) or forbid finding some faction-specific BP's altogether. Again, the problem is very clear, I don't want quality of my suggested solutions to undermine its importance.
Except none of them are "their" blueprints, they're all just from before the fall that they happened to have access to.
By that logic most of the planets and stations the various factions hold aren't theirs either, they just snatched them up when everything went to ***.
I don't think historical accuracy is of any importance for a faction claiming a BP as theirs, all that matters is if they can enforce their claim.
Not that I think this would work particularly well. If I'm fielding enough ships of a type a faction considers theirs to make them go after me I'm probably powerful enough to shrug off whatever they send. Still, it could add some flavor and probably wouldn't ruin the experience for anyone.
Except a lot of the ship are not build, they are salvaged. What is the hegemony going to do, shoot every shmuck that drag a hull from fringe space to the core? From what we see in vanilla, the core peace is tenuous as best, corruption is rampant and piracy is everywhere.
All it would really lead to is players stashing the mothballed hulls they find in one of the abandoned bases or another safe/neutral location's Storage until they're confident they can ward off the grubby hands of overzealous military/corporate agents trying to "reclaim" "their" property, anyway.
Ed: And come to think of it, surely this kind of interaction would lead to constant rep reduction pings, which would just be terrible in general. These prize ships can be enough of a headache to fully outfit early on anyway, so adding another reason that discourages players from experimenting with their new toy feels like a bad idea.
It would be better to make it a positive mechanic- something like AI Cores, where you can "donate" salvaged hulls to factions for a rep/credit boost, based on their condition/outfitting/subtype and such. A generic little shuttle that's half-beat up won't net you much, but if you turn in a pristine XIV Onslaught to Chicomoztoc then the Hegemony will be very grateful. It could also give you a reason to salvage the ships of deserters and haul them back rather than break everything.