They're all doubled, and they display funny (I'll describe that in a second), so when I tell Maya to display face normals it appears as though every single face, including those that shouldn't be, has its normals facing outwards.
The first image is the way the .obj file looks normally in Maya (once 'display face normals' is on).
The second is what happens once I click on the model.
The third is what happens once I deselect the model.
The fourth is what happens once I move the camera in any way, reverting it back to the way it looks in the first image.
Now, what's happening is every face is doubled, and the face that's immediately visible is facing the correct way, which I found by deleting faces and watching the normal indicator disappear, whilst the doubled face is orientated the opposite way, as if to represent what in SketchUp is by default the blue material.