How to calculate bind pose for bones that are not attached to the skin, but which are in a hierarchy where some bones are attached to the skin

Question

I have an FBX file with a model and what I am trying to do is write a converter using FBX SDK which would convert a given FBX file to my own format. The problem is that I am not able to get/compute bind pose for certain bones(the ones described below).

I can easily get bind pose matrices for the bones affecting a mesh from the FbxClusters.

I can also calculate bind pose matrices of bones which have no FbxClusters assigned to them if these bones have parent bones which have clusters assigned to them by the method described in the last post here: http://forums.autodesk.com/t5/FBX-SDK/Skeleton-Bind-Pose-for-bones-not-linked-to-clusters/m-p/417362...

Now the problem I am having is how to calculate bind pose matrices for the bones which have no FbxClusters assigned to them and which have either no parent nodes or their parent nodes have no FbxClusters assigned to themselves as well. (Please note that FbxPose has no matrices for these bones either)

In the image below I have outlined examples of such bones in red:

http://uploads.gamedev.net/monthly_06_2014/post-221385-0-43342600-1402961179_thumb.png

P.S. I know that an FBX file I am dealing with is correct, because Autodesk FBX Viewer displays and animates it correctly.