To appreciate how differently things are when you remove the rest of the universe, consider this: what if the universe is just one planet with the people on it?

As Prase said above, that depends on the boundary conditions. As the clearest example, if you imagine a flat empty Minkowski space and then add a lightweight sphere into it, then special relativity will hold and observers tied to the sphere's surface would be able to tell whether it's rotating by measuring the Coriolis and centrifugal forces. There would be a true anti-Machian absolute space around them, telling them clearly if they're rotating/accelerating or not. This despite the whole scenario being perfectly consistent with GR.