pedestrian: I also did a very quick check using alanback's 21-pointer against furbster. It was the first and only match that I looked at.

Of the 12 games in the match, 5 started with the same roll for each player, although the order of the numbers was different in 3.

Game 1   61, 46
Game 2   23, 42
Game 3   12, 31
Game 4   14, 51
Game 5   13, 31
Game 6   45, 54
Game 7   15, 51
Game 8   41, 42
Game 9   41, 41
Game 10   13, 41
Game 11   65, 63
Game 12   31, 31

If it's coincidence then it certainly seems to be one that can be found without much effort.

ps. Abigail's right about the odds. It doesn't matter what the first roll is, the chances of the second matching it are dependant on the 36 possibilities for that second roll.