Silas is talking about this:

Einstein suspected that if the whole universe was rotating around you while you stood still, you would feel a centrifugal force from the incoming gravitational waves, corresponding exactly to the centripetal force of spinning your arms while the universe stood still around you. So you could construct the laws of physics in an accelerating or even rotating frame of reference, and end up observing the same laws -- again freeing us of the specter of absolute space.

(I do not think this has been verified exactly [emphasis arundelo's], in terms of how much matter is out there, what kind of gravitational wave it would generate by rotating around us, et cetera. Einstein did verify that a shell of matter, spinning around a central point, ought to generate a gravitational equivalent of the Coriolis force that would e.g. cause a pendulum to precess. [Wow!] Remember that, by the basic principle of gravity as curved spacetime, this is indistinguishable in principle from a rotating inertial reference frame.)

Edit: You are correct from a classical physics standpoint that if you are in a windowless room on a merry-go-round, you can tell whether the merry-go-round is standing still versus spinning at a constant speed. (For instance, you could shoot a billiard ball and see whether its path is straight or curved.) This contrasts with the analogous situation in a windowless train car, where you cannot tell whether the train is standing still versus moving with a constant velocity.