What I've read is that the brain learns what the sight picture of a ball coming right to you should look like. When we run to catch a ball, what we're trying to do is line up with that sight picture.
Do you have some sources maybe? I find it very interesting, because it doesn't agree with my experiences.
I've never played baseball, but lots of basketball and soccer, and I get this "virtual trajectory of ball" overlay, so that I can adjust my body position, jump at the right time if needed.
Also often you look at ball, memorize where it will fall, then run to get there without looking at the ball. It can take seconds if it's a long ball in soccer, so it can't possibly be just adjusting to the sight picture.