I asked Brett this question recently and he told me it means that the faction you are applying to have inserted in that system must match the system's ruling faction allegiance (but not necessarily government type.) In other words, if you want to be an Alliance faction, the controlling faction in that system will have to be Alliance-affiliated. But he said the government type doesn't matter - so if you're applying to be a corporation, it's okay if the ruling faction is a democracy. Unfortunately, independent factions aren't exempt from this requirement.
This apparently wasn't always the case, but is how things are now, which is frustrating given that the turnaround time for a PMF lately is quite a few months! DNA-Decay does have it right - you might be better off just joining an existing group and sparing yourself the stress. It's definitely not for the faint of heart.