Many people are not aware that 3D Models are actually constructed using Triangle Faces. In the 3dsMax viewport it hides all these triangles and uses quads instead (which is what causes the confusion) simply to make modelling easier. You can view these hidden edges by disabling "Edges Only" in the object properties (see attachment).
I believe when 3dsMax creates the FBX file it includes all the triangle information used by other programs but also some unique to 3dsMax settings so when you import the FBX back into 3dsMax it will look the same as it was when you exported, however other programs will not be able to read this information and will just read the triangle face information.
I believe this is what's going on here...

--------------------------------------------------------------------------------------
Technical 3D Graphic Artist
Autodesk 3dsMax 2015 - Service Pack 4
--------------------------------------------------------------------------------------