A very simple counter example is that we can "see" the bend in spacetime made by the sun from how the earth makes a circular path around it, as opposed to going

A very simple counter example is that we can "see" the bend in spacetime made by the sun from how the earth makes a circular path around it, as opposed to going in a straight line. LIGO just looks at the path (or rather just the length of the path) of photons.