Due to the global spread of this game's participants and the responsibilities we have to all things outside civ, there's a likely chance that in these cases of war, someone, for whatever reason, won't be able to make their turn. A 20 hour timer coupled with a 10 hour rule, starts to become a 10 hour timer. Which, as we seem to be struggling with a 20 hour timer as is, becomes unreasonable. From my experience, fighting a war with someone in a different timezone can be a daunting task. His playing schedule may not fit with yours and vice versa, and then you end up with a guy not taking his turn until after midnight with the timer set to expire by 5:30 in the morning. And if you go and double move justifying your actions by following a 10 hour rule to the letter, the consequences can be so dire as to dramatically alter the course of the entire game.
Personally, I think it's unfair for me if some civ starts to get too powerful by exploiting an enemy with a double move. And for this reason, I would prefer them to be disallowed altogether, even at a cost of slowing down and even pausing the pace of the game.
I am familiar with two possible solutions to fix the double move problem.
1, we increase the timer in times of war and
2, we have an accomodating host that can reload any non-sequential or missed turns.
I would prefer the second option, although it greatly increases the responsibilities of the host. If we find ourselves in a position similar to my 5:30 AM example, we simply post in the thread and the host reloads at a more convenient time. Yes, it slows things down enormously, but I believe it's the best and fairest way to prevent the occurance of double moves.
The 10 hour rules work for prompt players and I do believe they should serve as a sort of guideline, but in no way used to justify a double move. However, here are times when a double move has no effect on the outcome, and in these occurances i think a double move within the 10 hour rule works fine. From this arises the question of whether or not it changes the turn order, which can have strategic affects (i.e., the espionage civ may prefer to be last if they are sabotaging production, etc.) but if the players involved can come to an agreement, or more likely, not put up a protest, then in these cases a double move is fine.
But again, I'd prefer that consequential double moves be avoided at all costs. Trigger happy players looking to cheat the system affect all of us, not just the immediate parties involved.