In Pose copy/paste case, (almost) all dependencies of the armature
object are cleared during the copy phase (only its obdata Armature is
kept). This would also clear ID pointers from the liboverride data if
the source object is a liboverride.
While manual handling of such cases is possible, it's simpler here to
simply make the data in the pastebuffer fully local, since only the Pose
part of it is used anyway.