how would you call it
 

Dont know the rule set, but I was a spectator at a 64 team multi level tournament which was OBVIOUSLY NOT ASA, and was watching a great 12U game.

No one on, two out. I was standing about 200 ft down the 1st base line when I heard BALL 4 then "DEAD BALL." The ball passed the catcher and found the only hole in the backstop and went into dead ball.

Next thing I know, the BR is being directed to 2nd base. I am standing with a parent I know and I am thinking. . THIS ISNT RIGHT.. . .(at least in my ASA understanding). Could this game possibly be decided on this bad call (NO COACH ARGUMENT). It was the top of the 6th in a Quaterfinals game. The runner stole 3rd and was batted in (the home team eventually won it in the 7th)

Is there any rule set that would have allowed the BR to advance to 2nd?

None that I have ever come across.

If memory serves, Dixie was 2 bases in this sitch. But it's been a while... a long while.

Edit to add... if the level of ball was such that runner stole 3rd - don't you think runner would likely have stole 2nd on the first pitch. So while the call may be suspect (not knowing the rule code used here), I doubt it altered the game.