I don't think two players can incur the time penalty on the same hole in match play. One of them had to incur it first and that player looses right then. Further actions do not matter. Sure, letting a player keep playing after the hole is over does not change the hole result. But that extra play could have an effect on the match in many ways. What if someone gets hurt while playing after the hole is over but they don't know it because the official kept it secret waiting for them to reach the next tee?
When it is over, it is over and there is no reason to keep it secret be it a time penalty or any other loss of hole penalty.
It's just a fact of golf that, at times, a player will have incomplete information. While I agree your example would be unfortunate, that situation could equally well arise if a player has not yet discovered that her opponent just made a stroke on a wrong ball.
I'm going to restrain myself from commenting on the time penalty any further. It's not necessary for this topic, the questionable copy of the rule that we had in the other thread hasn't been brought up in this one, etc.