This behaviour is not a bug by definition, because the AnimationPlayer is also an inherited node.
It is a known issue: in Godot 3.2 you cannot change the animation properties of imported 3D assets. You must name animations "name_cycle" or "name_loop" in your 3D modeling program. I actually worked with a developer on that during 3.2 beta because this feature didn't even work, so there was no way to make animations loop with fbx and gltf import via an editor.
For the record, you can and should be able to override properties on inherited scenes. It works in many cases, and not in others. There's a whole list of inherited scene bugs and known issues like these in Godot's issue tracker.