More specifically MM showed that earth is not moving relative to a hypothetical medium through which electromagnetic waves propagate. So either the universe is geocentric or there is no such medium.

Another interpretation is that the apparatus and not just light is made from ether — and so the signal is lost because the measuring apparatus is also subject to the local distortion.

That interpretation is also consistent with LIGO: we can detect those ether disturbances because the distortion of our motion on the apparatus doesn’t cancel the signal in the same way.