Could dark matter be "inside-out" reality?
As a disclaimer: This answer does not include references, and is mostly based on my first intuition when reading the question. I can see that it can potentially be an interesting question to discuss.

First, we live in a solar system, in a galaxy, in a galaxy cluster. That in itself means that there is a lot of matter around. We are also (at least very likely) living in an overdensity in the universe, meaning that there is extremely much matter where we are compared to the average in the universe. 

If we assume that we do live in an underdensity of the universe, that would mean that there is more matter present in the universe on average compared to where we are. However, if pockets of space in a distribution of regular matter was dark matter, then it sounds like there would be a larger amount of regular matter than dark matter in the universe, something which does not agree with our estimates. 

If we assume for a minute that it is the other way around (that we live in an area with a lot of matter, not a lot of space), then this theory will struggle with explaining some of the things that point towards the existence of dark matter. One such thing is the rotation curves of galaxies, which indicate that there is more mass presence than there is seen. I expect that there would not be enough space within a galaxy to create such "pockets" of space. Say, however, that we assume this was possible, then the voids we observe between galaxies and galaxy clusters would be even more gigantic pockets of space, which would mean that there would be an enormous amount of dark matter, which I would think would be inconsistent with what we see from the CMB.