This might be an issue with the depth testing. It looks like opengl does not care which object should render in front or behind.

Unfortunately I don't know how the SceneManager renders the object - is this a class you defined that uses the ModelBatch?

My suggestions are:

1. make sure depth testing is enabled using glEnable(GL_DEPTH_TEST) when rendering

2. use fbx-conv to convert a 3d model to a libgdx friendly 3d format. You may output a json formatted 3d model and inspect it further, to see if you get what you expect (of course, this is not practical for models more complex than ~a cube).

3. provide your own shader to libgdx. The default ones can look horrible.

4. try rendering a simple object, like a cube. If you still see rendering errors, then it's more likely a rendering bug rather than a model import issue / something else.