First off, obviously a T-rex would have to be able to stand up after falling. The idea that it couldn't simply because it has small arms is incredibly silly. Birds can get up without the use of their "arms" (wings) after all and being unable to stand up is a major evolutionary flaw.
Anyway, I've never seen anything that indicates it had a small optic center. T-rex, BTW, had binocular vision a trait among predators (although that alone doesn't mean it was primarily a predator). Also, many predators have very strong sense of smell including wolves. And of course, the only real major terrestrial scavengers in the world are gliding birds like vultures.
Beyond that, evidence has been found that shows attempted T-rex attacks on other dinosaurs. An example was a fossil that was found with a T-rex tooth lodged into its tail and the bone healed around it. Ultimately, everything suggests that T-rex hunted and scavanged like pretty much every other carnivore in the world.
It's not the arms but the weight of its body, if it fell over its bones couldn't handle it, especially its spine. Birds have hollow bones; the size/weight ratio is much different. The T-Rex had a sence of smell that puts Vultures to shame. Bats also have binocular vision its kind of a moot point. The attack on a living animal is cool but variable.
Other reasons for T-Rex being assumed a scavenger are bite strength & the presence of much smaller apex predators in Raptor packs.
Again not trying to call you out, dinosaurs were one of my favorite things growing up.
The vast majority of Bats are predators though and, despite common belief, they can see at night. And yes, T-rex has a very good sense of smell, but like it having binocular vision, I don't see that as ample evidence to suggest it is only a predator/scavenger.
Also plenty of predators have a very strong bite force like crocodiles and tigers. If you are talking about them crunching bones, Hyenas also are adept at doing so but they too are predators. Nor am I sure how the presence of smaller predators dismisses T-rex being a predator.
BTW, no problem. When I was a kid I was huge into dinosaurs as well.
All insectivore bats rely on their ecolocation to hunt, but can see. Fruit bats are the only bats to rely on eye sight. But that discussion is kinda off topic.
Ok here is my synopsis broken down.
1.) Super scent found in scavengers
2.) Bite force needed to get to bone marrow something only a scavenger of raptor kills would need
3.) A very odd hip joint that would make for a more long distance walker than a sprinter.