Well, do you actually have a camera layer? What are your preview settings? What effects? 3D shading settings? Lights? Layer styles? Adjustment layers? Collapser transformations? Comp settings? System? Just saying that it doesn't work the way you (wrongly?) expect it to work is pretty useless. From OpenGL issues to specific combinations of features breaking 3D rendering order there could be a multitude of issues be at play. You will have to provide a lot more info, including screenshots.
Thanks for a timely response! I figured it out, the answer was really simple: I did not have the "Active Camera view" on, which would have allowed me to see exactly how I was positioning my layers. I had it on "Front View" before. When is "Front View" actually useful?
Front, top, right, left, top and back are orthographic (no perspective) views useful for lining things up. Try 4views and you'll see how easy it is to arrange your scene.
These views are typical in 3D apps. Only the Active Camera, which is the top camera if you have more than one in a composition, will render. The other views will preview but only Active camera will render a movie.