Spent about 30 minutes hitting balls in the front yard. Started with slow backswings without a club, checking hip turn and head position at different positions. Then alternated between slow-mo swings and easy full shots for a while.
Aha! I had not considered that two competitors who were not partners would have any reason to collude; but, of course, the stricture is there to prevent two individuals from forming a battlefield alliance...so to speak. Kind of an anti-Pinochle rule. Thanks.
It doesn't matter the the partners are playing stroke play or match play, they may still choose which ball to play first if one of the team's balls is the ball that is away. See Rule 30 and 31. The key is that they are partners and as such they can assist each other in other ways with advice and strategy decisions, etc.
If they choose to play the nearer ball, then they still have the honor for the next play.
The prohibition is for individual play so that a player may not assist another competitor just because he happens to be a friend, or he has a wager on the competitor, etc. This stipulation only applies in stroke play if there appears to be collusion between the players. If playing our of turn is just incidental or to save time, there is no penalty.