I'm inclined to take Ansem the Wise at his word, that being said I always interpreted it as Quadratum being a world within the realm of unreality, not that Quadratum is a realm itself.
As for the theory of it being the real world I'm with ocean's rage on that, since we have real world locations in many of the Disney worlds as well. Though it would be pretty ironic to say it's the real world while being in "Unreality." With all the FFXV type vibes it was giving off, I feel like they were going for a similar "fantasy based on reality" type theme.