There are times you do not call what you saw. The truely great officials of any sport can do this.
I know that I have "seen" things that did not actually happen. I have "seen" things not happen that actually did happen. A great official can know what he saw and use that information to find out what actually happened. What actually happened may not be what you actually saw (most notably in basketball when a lot of calls are made without a steady base).
I'll give you an example. Had a call in a 15U game a couple months ago. I move to 1BLX for what I think will be a banger at the front edge of the plate. The throw came up the line, and I got caught out of position. The runner tried to avoid the catchers tag by running to the pitcher's mound side and stepping in to the plate. The catcher easily had the ball and was going to make an easy tag. As the runner passed the catcher, his hands came down (to where I could no longer see them) in a non-running motion. They came down quickly, right into the area the tag was going to be applied. 2 open hands. And then I saw the glove and the ball on the ground.
Now, did I see the INT? Nope. Did it happen. Yes. Did I call it. Yes. Very bold call, met with much aggravation from the offensive manager.
After talking with BU in the parking lot, he said it was obvious, and I got the call right.
Now, the opposite logic... had a play that I saw perfectly and passed on a call, because I had doubts whether it really happened. I'm PU, runner rounding 3rd. Coach puts up the stop sign, and reaches out and, from what I could tell, physically assisted the runner to stop and get back to 3rd. Now, that's what I saw. But I passed on the call. Why? Because a) I had this coach for many games and he's not an idiot b) There was no play anywhere on this runner and no reason for the coach to do this and most importantly c) I realized that what I saw might not have actually happened.
Asked BU about it in the parking lot, said that the coach absolutely did not touch that kid. He had the line of sight where he could "see through the play" where I was straight-lined. If I had called what I had saw I would have been dead wrong.
So, you can't always call what you see. And you can't ignore what you don't see. You have to use what you see to help you figure out what really happened. 90% of the information we gain comes through our eyes. The other 10% comes through our other senses (hearing definitely), our logic, our anticipation and readiness for a play, our understanding of call sustainability and the limitations of the position we were in to officiate that play, and a degree of common sense.
I might have just confused myself
If this makes any sense please let me know so I can pat myself on the back.