Factions with very low levels of influence (<5%, iirc) can't start a conflict. Civil wars start when the influence of two factions is brought close and maintained there, or when another faction reaches (again, iirc - the trigger has been changed) >65% influence.
If the Nobles of HIP 10716 are at 1%, they're pretty much untouchable by the influence parity mechanic. If there is a faction in the system that is over 70% or so, I'd suggest that the push past the percentage that triggers a conflict was too fast, and that therefore the influence would need to be pushed down and raised again to trigger it. Given that it's a grinding system, I doubt very much that it will happen - it will require co-ordination, and interference in the form of rank-grinders not interested in the political shape of the system will likely nullify anything that isn't really large-scale.