Would the perspective difference be significant even if it were far out into the solar system?
Spin up your mental model of a circle in 3D space, look at it from a vector perpendicular from its diameter, rotate it 90 degrees in any other axis but the one you're looking at it; on that 2D projection, it will be a line.
Right, and as a matter of fact that's exactly what we DO see with the Milky Way galaxy. It can be conceived of as a circular disc, more or less, but in our sky we see it from the side, as a streak or a band rather than a disc.
> They also didn't check if other stars would form circles from any arbitrary point of view (how many circles are actually up there, not just the apparent ones),
I think (not sure of the proof) that any set of points that form a circle from a specific PoV would, from any arbitrary PoV form a regular shape (ellipse) or a straight line.
So we can probably tell if any group of stars/galaxies/bright-lights-in-the-sky form a "structure" (i.e. a regular shape).
If you think about it, it doesn't matter which point of view it works on, if the thing is an actual circle that's interesting on its own, or presumably a sphere(?) but they don't even touch on that because "3D is hard"? Anyway, for some reason they implicitly choose our point of view as the "interesting one", funny (/s, actually lame and sad) to see the geocentric model is still alive after two millennia!
They also didn't check if other stars would form circles from any arbitrary point of view (how many circles are actually up there, not just the apparent ones), which would be a trivial calculation, but I guess "matrix transformations are hard" as well?
The whole paper is pretty weak. They calculate the "thickness" of this "circle", i.e. the distance from the galaxy closest to us to the galaxy further from us if you undo the projection; and they come up with a value of ~400 Megaparsecs. Now, you may be inclined to think "yeah, but the universe is HUGE and on that scale they may be kind of tighly packed?". Nope! It's on the order of the largest (actual) cosmological structures that we have identified, so, pretty much, they are as further away as they can be from each other, lol.
This is pretty much astrology.
Source: I read the paper.