The wraiths could perceive living beings and to a certain extent even interact with them. They were simply disembodied spirits. However, as all spirits came ultimately from Iluvatar, and as they would be a part of a, I cannot find fault with your conclusion that Morgoth could somehow shape that aspect of a which Gandalf referred. But there was no need for him to do so. The disembodied spirits simply had their own means and levels of perception.
Perception differs even among living beings.
Dogs have an incredibly sensitive olfactory system compared to humans, for instance, and many insects have terrible eyesight. There are creatures such as bats and dolphins which see but navigate better by sound. The terminology, without benefit of supporting examples, is insufficient to conclude there was such a separate reality. We have no indication of what the division stems from. From the available evidence the matter is very debatable.