Quite a few colonies were founded by groups who raised the money by selling everything and fleeing in barely sail-worthy ships with dubiously adequate quantities provisions of even less trustworthy quality.
Others were essentially dumping grounds for undesirables - literally taking religiously or politically undesired segments (like homeless and criminals, or in the case of Liberia, former slaves), and shipping them off with token provisions.
I recall few if any colonies founded over the specific objection of the home government. The point, if incompletely stated, was that the home government remains a brake on what can or can't occur within territory it lays claim to - at least so long as the home government retains the will and resources to maintain oversight.
Pournelle's milieu paints a picture of individuals leaving Earth to found their own utopian societies only to have Earth's government force them to accept large numbers of undesirables. Some historical colonies faced similar issues: once they'd blazed the trail, they found themselves attracting folk who were not exactly of the same caliber as the founding group, and they faced a certain degree of meddling from the home government. Conversely, as the founding settlements grew stable and people began moving out from those, secondary settlements would evolve that were less controlled by both home government and founding settlement, sometimes creating problems for both the founding settlement and the home government.
Traveller presents some unique challenges in that much depends on the quality of the colony world and the nature of the home government. If it is sufficiently habitable, people can settle the hinterlands with little effort and effectively place themselves beyond the scope of the home government or founding colony - but technology can make it very difficult to completely escape the eyes and ears of a sufficiently intrusive and well-equipped authority. If it is not easily habitable, the cost of creating habitat can make it difficult to grow beyond the reach of the home government's overseers, but the cost of delivering and sheltering overseers and their guards may preclude effective oversight. Then there are the influences of megacorporations and other external powers to consider. The situational factors are diverse enough that it's difficult to envision a hard-and-fast rule that could cover all potential variables with any degree of verisimilitude; a random roll and some well thought out after-the-fact rationalization tend to be the simplest solution.
I'm also frankly not entirely clear on the authority of a main government with respect to all the little rocks and pebbles within its system. The UPP reflects the dominant world in a system and by extension implies that the dominant world is, well, dominant in terms of interaction with other systems and the Imperial government, but that's not the same as saying the dominant world has authority to extend its jurisdiction to every nook and cranny in the system. It's one thing to suggest a world has authority over its citizens and corporate "persons" who settle a nearby moon; it's quite another to suggest its jurisdiction extends to a distant mining colony founded with and defended by the resources of some megacorporation or other foreign interest.
On the one hand, an Imperium with thousands of years experience in the founding and settlement of colonies is not likely to embrace customs that put homeworlds and colonies in the same system on an inevitable course for eventual violent conflict. On the other hand, the megacorporations and the Imperial economy as a whole have a powerful interest in limiting the jurisdiction of planetary governments so that exploration and exploitation of potential mineral resources in the distant reaches of a system can be conducted without undue restrictions from planetary governments that may not have the wherewithal or technological means to exploit those resources themselves or to assert their political will beyond their own orbit.
I'm curious what examples we have that might speak to the issue.