If false, this could be easily falsifiable with a single counterexample, since if true, no coin tosser, human or robotic, should be able to do significantly better than chance if the toss is reasonably high.
EDIT: according to this
In the 31-page Dynamical Bias in the Coin Toss, Persi Diaconis, Susan Holmes, and Richard Montgomery lay out the theory and practice of coin-flipping to a degree that's just, well, downright intimidating.
Suffice to say their approach involved a lot of physics, a lot of math, motion-capture cameras, random experimentation, and an automated "coin-flipper" device capable of flipping a coin and producing Heads 100% of the time
the premise has already been falsified.
The link discusses normal human flips as being quantum-influenced by cell-level events; a mechanical flipper doesn't seem relevant.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.