Just moving this Cheversi discussion from the Requests Board to here, so if you would like
to read the preceding posts, thats where they are ;)

AbigailII/Perfect information:
Say White has three equally good moves A, B, and C and Black has the Moves X, A',B' and C'.
X garanties a draw, A', B' and C' win against A, B and C respectively, but lose against the other two.
So Black should play X, but he might choose to play a mediocre move and get lucky and win.
In case of simultaneous placing of pieces, a player cant know the outcome of a game anymore
by solely doing enough calculation, so luck comes into play, hence there's no perfect information anymore.

AbigailII/Swap rule:
Of course in your example a swap rule wouldnt help.
That's because in that game there are no positions that are drawish.
But thats not the case in Cheversi.
If after any of White's possible first moves, Black is able to construct
a drawish position with his first move, then adding the swap rule after move 1
would cure the imbalance problem.