If an unambiguous centre point did exist, then flipping the coordinate system from (distance to centre point, point on a n-1 dimensional hypersphere) to (1 / distance to centre point, point on a n-1 dimensional hypersphere) would be a trivial and uninteresting transformation. In other words, turning the universe inside out does nothing to decrease (or increase) the difficulty of choosing a centre point.

This transformation is its own inverse. Applying it to the coordinate system in the article we find that the author has chosen the centre of the planet Earth as their centre point; that is what makes their coordinate system possible. This is totally arbitrary and does not solve any deep mysteries. The stuff about turning the universe inside out is just waffle on top of that.