what if the Earth wasn't moving, but was stationary in the center?
Indeed, the conclusion reached by the experimenters is that, "If the aether exists, then the Earth is stationary to it within one part in such-and-such." Galilean relativity had been accepted long ago, so no physicist worth his salt would say "stationary [in the absolute sense]," but only, "[relative to such-and-such other object]". The "[]" mean: maybe it's implicit what it's relative to.
However, geocentrism was disproved by Galileo when he observed that Venus had a full complement of phases and is sometimes closer than, and sometimes farther than, the sun. This is not possible if Venus revolves around the Earth, rather than the sun, but is perfectly predicted by the heliocentric model. Therefore we are left to conclude that the Earth revolves around the sun.
Given this, and since the Michelson-Morley experiment equivalently requires that the
sun is stationary with respect to the aether, we are forced to conclude that there is no aether.