[Andy]

Jeff - coach your players to run to first if there is any question in their minds.

As a Plate Umpire, this is not always easy to see. As you mentioned, the batter may be turned with her back to us and our view is blocked. You can always ask the umpire to check with his partner (if there is one). But, if I have to check this with my partner then s/he is not doing a part of their job. I expect my partner to call this immediately if I do not. As a base umpire, if I see the batted ball hit the batter, I will wait a split second to see if my partner calls it and if he does not, then I will step in and make the call. I am only going to kill the play, it's up to my partner to determine whether or not the batter was in the box.