This has been there for a very long time. Whenever importing FBX with skeleton/armature from other apps, many times It's completely screwed - bones are rotated in wrong directions and rotations are wrong. Looks like coordinate systems are not converted correctly.
In this case - perfectly normal skeleton from Maya (From actual project where it is used in production in Maya, Unity, Motion builder etc).
Blender: All versions
OS: All OS
While I cant very the file in another program atm (could do tomorrow) I can confirm the output in blender looks unexpected [tried a couple of settings with no luck]
Hate to ask, but @Bastien Montagne (mont29), could you have a look?
Using Force Connect Children and Automatic Bone Orientation will help. Besides that, yes, upper part of the skeleton is weird, no idea why. Probably some issue in Pose/bind matrices somehow, armature model of FBX is so complicated…
I'm experiencing this issue with the importer (100% of FBX armatures I import fail to import correctly).
After spending a while looking into it, what appears to be happening is the importer is ignoring (or not successfully using) the PreRotation and PostRotation properties from the FBX LimbNodes to give the bones in Blender the rotation they're supposed to have. When the bones are getting created by the importer, the bones are successfully given proper lengths however the bones aren't getting rotated at all so that the bone tails actually wind up where they're supposed to. I'm not 100% sure about this, but from the reading of the python code I've put in I believe somewhere in the following line the rotation information using the PreRotation and PostRotation info is either not being considered or not being correctly applied:
from line 1931 of import_fbx.py
"# And rotate/move it to its final "rest pose".
bone_matrix = parent_matrix @ self.get_bind_matrix().normalized()"