There are plenty of example of statistically reliable effects in the embodied cognition literature. Stimulation of motor speech areas modulate performance on speech perception tasks; reading sentences about closing drawers makes one faster in generating pushing movements; [insert favorite result here]. Let's assume all of these effects replicate. I have no particular reason to doubt them.
I do have a problem with the knee jerk interpretations though. Motor stimulation modulates speech perception, therefore, the motor system is critical for speech perception. Comprehending sentences about pushing facilitates pushing actions, therefore, motor acts of pushing are part of the concept of pushing.
It's a faulty inference.
The same inferential error has been recognized and called out for lesion work: just because a brain area, when damaged, causes deficits in ability x, doesn't mean that the brain area is "doing x". Bilateral visual cortex damage will cause naming deficits, but isn't the neurological seat of naming.
A lot of work coming out of the embodied cognition world is making the same inferential error, I suggest.