The medium plays a part in the momentum transfer, yes.

The net force on a spherical body isn't zero for a single beam because the beam changes shape moving through it, so the refractive details are different on either side.

But for two counterpropagating beams, which is what I used, the left–right forces do balance out, leaving an internal tensile load that stretches a compliant medium. You don't notice this in everyday situations with macroscale objects because they're stiff and the light is weak.