Thank you for clarifying this! I would suggest the following modifications to export_fbx_bin.py at line 1923:

Sorry for assigning, I don't use the bugtracker too much. Won't happen again :)

I had the same problem (Blender 2.75 MSI install, Windows 7 64bit).
I used "blender -r" command (run a command prompt, navigate into the application folder and give this command)
It shows that registry was successfully updated, but still nothing happens. You should manually set in the explorer, that blender is the default application to open .blend files with (right click on a blend file, run with, choose application) Before "blender -r" blender doesn't show up as an option and which was worse I couldn't associate blender.exe from the program files folder either.

You might be right, FBX Converter can not view the exported file but converts it without problem.
Meanwhile I tested the raw export in XSI 2013 and Maya 2013.
XSI imports its first UV, but "thinks" that the second UV should be a spherical projection?!
Maya imported it flawless.
I have asked our lead coder which version of FBX SDK we use in our proprietary tool. It is 2011.3, which should be a few versions behind blender's exporter (could not import the file at all).

I use the latest version of the FBX Converter (2013.3). To be sure I have downloaded the latest version right now and reinstalled it. I have downloaded the latest build from the buildbot too (blender-2.70-7d64054-win64.zip). Does not help. FBX Converter loads that simple scene I attached to my last comment, but it is empty.

The problem still exists if I select 6.1 ascii. (UVs are at correct place but connected weird on the second UV set)
7.5 binary does not work at all. Autodesk's FBX Converter can't handle it (even with single UV set!!!).
The last official version was 2.68a which generated working FBX export.

I did some more testing. Results attached...

I have downloaded a build right now, to test it. The 2nd UV is still messed up in the export...