I took a look at the fbx file in Max(and also in UE4) and it looks like the UV’s got somehow messed up during or before export. If you import the fbx into Max and apply a checker texture you’ll see the same issue. When you open the UV editor and select faces they dont line up properly. They look as expected but there are actually overlapping faces.
When you get back and still cant fix it, can you save and upload the Max file as 2014 please?