For the result to be different, the real world would need to have a different sort of topology. For example, if we lived in a non-Hausdorff space, the result would potentially be different. A Hausdorff space is one where for any two different points, you can take a small ball around each point, and the two balls won't intersect. A non-Hausdorff space is just a space where this isn't true for at least one pair of points.

So, for example, if wormholes are real, the space we live in might not be Hausdorff. And if you had a wormhole sewn into your shirt in the right way, you wouldn't be able to turn it inside out.