As with all other player responsibilities, this only applies with regards to submission of acceptable scores for handicapping. Since our hypothetical group are not doing that, they are free to do as they please.
So lets say this hypothetical group is 29 players and they play a Friday roll-up stableford with 100% course handicap. Only one player has a course handicap below 11.
The following day they play a club organised stableford (non-qualifier) where they all play off 95% course handicap. The single figure player plays off the same handicap, but all the others play off one shot below what they did the previous day.
Is the single figure player suffering no advantage or disadvantage in both scenarios?
I would say that the only way to be sure that no wrong doing (unfair advantage) is occurring is to apply the correct playing handicap for individual strokeplay on both days.
This dilemma does not occur in Australia, as there is no course handicap.
The only way for there to be no dilemma here is to apply the correct playing handicap for individual strokeplay "at all times".