E=mc^2 .... bidirectional?

[PeterDonis]

you need to specify how you are defining "space" in order to measure a spatial distance.

Yes, and the underlying assumption being made in this case is that the "distance" being measured is the distance that would be measured by stationary rulers, i.e., rulers that are all "hovering" at a fixed altitude above the black hole. Or, if we want to be really pedantic and eliminate the effects of proper acceleration on the rulers, we can arrange to have a family of free-falling rulers all come to rest momentarily relative to the two circles, in just the right way to lay end to end along the radial line between them.