As I understand, we (currently) have no way of verifying whether light travels at the same speed in different directions. However, if it did, would we not observe "skewed" black holes? If the speed of light were smaller on one side of the black hole, the photons passing around that side would have a bigger minimal radius of rotation around the black hole than the photons on the other side. I.e., photons could get closer to the black hole without getting sucked in on one side than the other. Thus the black hole would appear bigger on one side than the other with respect to the center of mass. I am imagining something like this
Moreover, by one theory light moves instantaneously in one direction and at speed of c/2 in the other, would we not actually physically see the black hole in this case? Am I misunderstanding something?