Radical embodied cognition is committed to the idea that perception involves some form of "pick up" of information from the environment. The mind constructs nothing. Therefore the percepts we have must be direct reflections of information that is in the real world. For example, our percept of a cup is the direct result of light interacting with a unitary object that has a definite location in space.
If it turned out that in the actual world there was not unitary object corresponding to the cup and it had no definite location in space, there would be a significant mismatch between what exists in the world and what is perceived about the world. Therefore our percepts of a unitary cup in a definite location must be a construction of the mind.
If the above assumptions about REC's claims are true and we indeed found that the world is such a weird place as in the example, then REC must be wrong. REC is committed to a fairly standard view of a veridical space-time world.
Quantum physics has revealed that a standard space-time world does not hold at the particle level. So if we lived in that world and took our perceptual measurements in it and if we perceived particles in definite locations (as seems to happen when we measure them with our instruments) then we would have to assume that perception is constructed and not just a direct pick up of information. REC would not be a viable theory at the quantum level.
Recent work in physics has suggested that something like quantum weirdness applies also to the very large, that space-time doesn't exist at all. If space-time doesn't exist then that cup is not a 3D object fixed in a particular location in space, despite the fact that my perception tells me it is. And if this is true REC is a dead theory.
Put differently, if ecological psychology wants to be serious about the interaction of the physical world and the body giving rise to all things human, then it HAS to take discoveries in physics seriously because that is the means by which the true nature of the world can be revealed. In this sense, REC can be falsified by developments in physics.