The way to think about it is the principle that: The idea of the Swiss system is to find a fair set of opponents for each player in the tournament in a transparent manner.
Malcolm Clarke wrote:
This may be a recommended solution, but is not one I feel particuarly comfortable with. I would prefer not to have the draw for all five rounds made by the start of round 1, with it known in advance which players are having three whites in the competition.
Taking the above principle, an All-Play-All generates the same set of opponents as a Swiss. So there's no need to make life difficult by pairing them, with the risk that you may reach round 5 with no set of legal pairings. You just toss a coin to see whether you do the pairings Jack showed or reverse them all, and off you go.
Malcolm Clarke wrote:
More posts have been added sinse I was compiling this, and I have also seen Alex's recommendation for 8 players. However I personally would find that solution a bit on the random side.
Again, taking the principle, if announced in advance, this system is transparent. In both cases, you play all opponents bar one. I think that if you choose this person randomly via the APA minus one trick, or via convoluted Swiss pairings, I don't see how the fairness of the opponent selection increases by choosing one or the other.