I can't believe there even was a reroll.

Of course it doesn't count - there never should have been a reroll. The first roll is fine.

Were the participants inhaling or exhaling? Of course, if it was one of each that could be problematic unless they were equal distances from the area of the die roll.

Well Darth Jim, I remember that at least I was holding my breath, because this roll would decide the whole game. I'm not sure about knapp, but he was the one who rolled it, and called for a reroll. I'm pretty sure that if it would have been a hit, he would have never called a reroll, and neither would I.

I do not think there should be a reroll in this instance.

But this reminds me a bit of another incident that has left a bad impression from a GenCon national championship event a few years ago.

A guy rolled the dice that ended up off the map (still on the table right next to the map with no interference and clearly readable). He ended up missing a very important hit, which was an an obvious game changer at that point in the game. He asked is opponent if he could reroll because he always meant to roll on the map. For some unknown reason the opponent said yes (probably just trying to be a good sport, but I would have said no way and called the judge over if he complained). Anyway, the reroll hit and he ended up winning a game I'm pretty sure he would have otherwise lost.

I watched the map roller the rest of the tournament and the dice regularly rolled off the map and he didn't seem to mind or notice.

Anyway, I appreciate everyone's point that if the roll is random and there is no interference from a person and the dice is obviously not skewed or unreadable, it is a good roll. Confirms a good point of reference for the future.

This can always be a problem with dice games. I find it best to state conditions of dice rolls before dice games every time.
What I use:
1) All prerolls are null and void. (This prevents people from practice rolling, then keeping a good roll 2seconds before they are legally allowed to roll)
2) Unless it is a tilted die, All rolls that are on the table count. If you accidently dropped the die, that is your fault. If you hit something with the die, why did you aim your throw that way? If you hit someone's hand, why did you throw the die that way? Put on your big boy pants and learn how to roll a die and accept what number comes up.
3) .....or just use a dice tower.

We used to play that if the dice hit any figures on the board it was a reroll. But that's only because one of the kids we used to play with would sometimes get confused and think he was bowling for minis