Made a similar call a couple of years ago during a college baseball game as the plate umpire.
There were runners on so my partner was inside the diamond. The hit, with the home team behind in the bottom of the 9th, was a big curving fly ball down the 1st base line. I hustled almost as far as 1st base and made the four base signal that ended the game with the home team winning. The ball hit the ground 30 feet foul.
The visiting coach went nuts - they always do. He wanted to know how I could make that call. My response was quite simple and he shut up immediately... "Because I saw the ball go behind the foul pole." The foul pole in my situation was probably 40-50 feet tall. Your situation sounds much more difficult and perhaps the ball was above the height of the foul pole making it extremely difficult to decide whether the ball went out in front of the pole (which the 3rd base ump must have felt happened) or whether it went out behind the foul pole.
Tough call, but one coach or the other coach was sure to go nuts...
They always do.