Frame violations, depth budgets and floating windows

I think that the reason the Rift avoids some of these issues is because it's designed as a screen at the depth-distance of your eyes. It isn't really possible for things to be "inside of" your eyeballs because then you wouldn't see it at all (and in 3D games, such objects would get nearclipped so they'd also be invisible). Thus, all of the depth involved is "on the other side" of the screen.

You are correct - no frame violations or depth budget here.

It's important to understand that the work that goes into rendering a 3D scene for the Rift is also fundamentally different than the work that goes into taking a 3D picture. Whereas traditional stereoscopic photography uses "toe-in" stereo, where cameras are rotated inward to establish a focal plane so you can project objects in front and behind it, the Rift has a focal plane fixed at infinity (someone did the math and, if I remember right, came up with it actually being around 300 meters) and uses parallel axis asymmetric frustums so that objects only appear in front of the focal plane.

The result of that paragraph long sentence is that the Rift doesn't suffer from convergence issues that are created because rotating the cameras inwards causes slightly an incorrect perspective for each camera - particularly for objects that are close. One such effect is keystoning, but it also exacerbates the floating window effect (remember, the edges of the screen are effectively a region where one eye is "correct" and the other eye has maximum perspective shift) and issues with depth budget. The Rift, by virtue of using a significantly more correct approach to stereoscopic 3D, simply doesn't have the same problems and as a result feels more natural.

You can, however, have frame violations. In general, if you are rendering a scene that enforces depth testing you will never see it, but for items like the player weapon and the HUD that you generally want to always be visible it may not be possible to render them "properly" without them being culled from your view. Half Life 2 and TF 2 both exhibit this issue if you face a wall and walk up to it.

Anyways. The TL;DR: is that these issues are much more predominant with traditional 3D photography/video is because they use a whole slew of bad techniques to create the stereoscopic effect. As the Rift uses a significantly more proper technique it mitigates it. You could, if you really wanted, recreate these inside the Rift. In fact, some of the worst demo's I've seen that took shortcuts in rendering did have some of these problems.