You know why it was a fair ball......?
Because the umpire said so. PERIOD.
The entire base is in fair territory. Any part of the ball bounding over any part of the base makes it fair. But in the end it is the umpire's judgement that determines the call and generally he is 60-100 feet away (10 feet behind home). So it is pretty much a guess but hopefully he used proper mechanics and made a reasonably good and defensible guess.