The FBX SDK is free, but the format is considered a "Closed Format", which means you can only open FBX models in software programs that have added the proper SDK API. This is a bit of a problem for Blender.  Blender is GPL licensed, which means it can't link to "closed source" libraries.  Software applications that use the official FBX API tend not to have any problems, but that wasn't possible with Blender's license. 

Blender has done a great job recently at adding FBX functionality without using the FBX SDK, but there will be some things that aren't going to translate as perfectly as they would in the Autodesk API ecosystem.

Regarding the Better FBX Importer and Exporter addon, I'm not exactly sure how they did it.  Perhaps they're using the SDK somehow or maybe they've reverse engineered it?  I know from other sources that it is updated constantly to keep up with changes or add new features to the existing FBX integration.

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