The RNG function on BGA is a server-wide call. IE, for every game that requires a random number, the function is called when that game needs it. In any given second, it may send 4 dice to Can't Stop, 2 dice to backgammon, 5 dice to Seasons, a deck shuffle to Race for the Galaxy, 4 dice to a different Can't Stop game, a board setup to Chess960, etc., etc.
The fact that your opponent rolled X doesn't mean that you would have (considering the microsecond delay in saving the progress earned and switching the active player). It just means that you'll remember it more, and think the dice and the site are against you.