If you look at the quick reference card that somebody posted in this forum you will see they have a different opinion. I was just trying to reconcile the different opinions. I agree with the answers provided above.
When both players' figures are on the same space, the player whose turn it is may force both players to reveal their encounter cards in the supply.
This is true only if the player whose turn it is has just moved into that space. If player's figure starts a turn in the same space as the other player's figure, he can force the revelation only by moving the figure out and then back in again.