Good spot! That is the product working as intended though. The background doesn't exist except as an asset that replaces the green screen. The tool is meant to replace the green screen without the need for manual rotoscoping. Even in a traditional process, the distortion needs to be done by VFX as a separate process. To do that though, they still need the green screen keyed out and this tool does that.

True, but with visual art there is what is correct and what looks correct. When things are moving and the area small no one is going to notice.

But now that is problem is solved a director will come along and say... I want a scene with a big glass of water and the camera will zoom in on it and will see the monster refracted through the glass.

When you watch the video it becomes pretty clear why it wouldn't be able to do that, although it's fun to think about how a future iteration or alternative might be able to credibly (if you don't look too hard) mimic that someday.

I wouldn't call it a bug. This is a first step, not a final step. Maintaining the refraction might be more realistic, but it's not necessarily what the creator wants.

You’d have to track it, render it, and comp it in. It’s not ridiculously difficult, but there’s no way that’s going to happen automatically.

Sure, because they used monotone backgrounds and never really captured any distortion.