Why does stabilizing the image make it any more or less apparent?

I think it just means it removes the distractions of the grain and shaky camera.

But really, it was always evident it was a guy in a gorilla suit.

You can see the link I posted (https://youtu.be/Vsj0vK8LjVk). To my eye it makes it more clear that it is just a dude walking like any human in a costume would.

I don't recommend it, but there is an image-stabilized Zapruder film out there that makes the Kennedy assassination a good deal more shocking/gruesome. You've been warned.