No, not photoshop. Zbuffer is 3D pipeline thing. If you use OpenGL or DirectX for 3D, i.e. if you have an option to enable such 3D modes, it'll likely use it, and even if enabling software graphics pipeline for 3D such as available in Carrara, you typically have a Zbuffer to sort the depth of pixels being rendered.

 

To me it just looks similar to wat you get when Zbuffer is either disabled or not working: there's no sorting of the pixels, so they appear in any order. Typically the order in wich they're being rndred from the mesh in the 3D scene.

 

If the model was created in Wings, it may have its influence as to which facets are drawn first and next and last but the Zbuffer is responsible for showing what's close and hiding what's far and hidden. When it's transparent, all should appear to some degree. But the Zbuffer is still needed.

I'd look into Bryce settings: are you able to determine which 3D pipeline it should use? are you able to enable/disable Zbuffer in that choice? are you able to switch to another pipeline like software or OpenGL or DirectX and see any change?

Is it doing this on other computers too?