I'm guessing they're facing the pilot in the direction as the thrust because they know the human body handles Gx better, and the pilot's frame of reference is being used for x, y, z. Since negative Gz is described as the awful one where all the blood rushes to your head and your eyelids swell up. But this is totally inconsistent with how your orbital sim is handling the directions, of course.

I think you're right about getting hit in the stomach being reasonably safe and kind of plausible. Note that negative Gx is slightly different from positive Gx in the NASA article, but my impression is that the body basically handles it similarly, we just don't have as much data because we don't do it as much, since pilots like to see where they're going. It doesn't sound like Chat is piloting so that's less of an issue.