[cowbyfan1]

I look at it this way.

If the ball and the BR arrive at about the same time and the BR foot misses first base, call him out immediately. If the runner is clearly past first I would do nothing and wait for an appeal or runner to touch first, then make the call, one way or the other.
My thinking on this is if the runner had rounded first and went to second, it is obvious he is safe at first, unless by the appeal. With a "banger" at the bag, it is easier to sell it. If the coach comes out and argues, you look him dead in the eye and say "Coach, your runner has still yet to touch first base" That would, more than likely, end the arguement right there.