This is a likely interpretation.
Alternatively, it could mean as noted above that Frontier Worlds out on the fringes are still granted some special privileges and additional leeway and home-rule provisions that go somewhat beyond that of the standard member-world contract as practiced in the Old Core Worlds of the Imperium where entrenched nobility and Imperial Core cultures and societies have held sway for countless generations (or millennia).
Except that by the time the Imperium offers a world membership on the frontiers, the megacorps usually have some influence and when a world joins that world is assigned a noble, usually from the planet's population, as its representative in the Moot. What I mean to say is that the world already has some connections to the Imperial power structure by the time membership is offered.
No world is forced into Imperial Culture... or 'starfaring culture'. The Imperium doesn't require it other than obedience to Imperial High Law and non-interference in those activities regulated by the Imperium. The vast majority of the population doesn't have contact with the outer starfaring culture and couldn't care less. Travellers contact it a lot because Traveller's activities extend into those areas where the Imperium brooks no interference... trade, defense, criminal activity, etc. But 90% of the population of Regina, Rhylenor, or Mora have almost no contact with the Third Imperium at all. These are issues for the world government, the Starport Authority, and the noble representatives to deal with.
What assimilation that does occur happens by 'soft power' means... entertainment offerings, museum exhibits, speaking tours by notables, etc. And all of that is easy to skip, ignore, or avoid by the average Eneri Smith on the street.
In matters of defense of strategic frontier worlds, the Imperium spends a fair slice of the Imperial tax base fortifying 'anvil' or 'fortress' worlds like Jewell, Efate, Regina, etc. This allows these worlds to have larger system squadrons, extensive meson gun arrays, larger armies on the ground etc.
This is also a form of influence and assimilation. All other things being equal, a world with a long history of loyalty and obedience to the Imperium and its policies will receive greater investment from Imperial taxes than one that does not have this history of cooperation.