If I could take a moment to weight in, I don't believe the original posters problem is related to FBX. I have run my own tests with complex and unusual organic meshes and I don't see a problem with FBX 2013. What is more likely is that their artists using Maya do not realize faces are set to "two sided" shading by default. When they are exported into Max, who uses "one sided" shading by default, the mistake becomes more apparent.
If the original poster is still around, and want to test my theory, you can download the newly released Maya "Bonus Tools" and select "Display" -> "Toggle One/Two Sided". Cycle through that a few times and watch for changes. It's very easy to make these mistakes, and I know about this one from experience. 😃
-Avotas