None of the previous answers worked for me. Here was my solution:
-The parent group includes transforms which need to be matched
-Unparent breaks transforms on the mesh. It needs to have the same transform as the parent group. Do this by RMB-ing the rotate X>Unlock selected
-Re-lock the same property/transform by RMB (the transform)>lock selected
-Select the root bone, then the mesh>export the .fbx
*If there are any edits to the mesh, make sure to run edit>delete all by type>non-deformer history (before exporting)