You did it exactly right. Your partner is having a brain fart. He should be trailing the Batter-Runner towards 1st for that very call... and he should be doing it with every batter unless there is a potential play coming to 3rd or home. The PU is surely in the best position to see if F3 pulls off the base
towards you to make the catch. If the throw is errant to one side or the other, or up, you should have the best look and can sell the call without his aid.
It is absolutely an imperative mechanic for 2-man. And as such it may not always get discussed in your pre-game... BUT IT SHOULD. I'll bet it does get discussed in your next pre-game.
For your situation the PU should have been half way to 3rd for R2's advance but he is still in great position to see a pulled foot.
Good job! Stick to your guns and discuss it in your pre-game.