I'm honestly not sure. I find myself confused. According to the article, they say:
They also point out that it would only take one counterexample to falsify their idea – a use of classical probabilities that is clearly isolated from the physical, quantum world.
But what would that look like exactly? Naively, it seems like the robot that flips the coin heads every time satisfies this (classical probability: ~1). Or maybe it uses a pseudo-random number generator to determine what's going to come up next and flips the coin that particular way and then we bet on the next flip (constituting "a use of classical probabilities that is clearly isolated from the physical, quantum world"). But presumably that's not what they mean. What counterexample would they want, then?
The authors claim that all uncertainty is quantum. A machine that flips heads 100% of the time doesn't falsify their claim (no uncertainty), and neither does a machine that flips heads 99% of the time (they'd claim it's quantum uncertainty). As for a machine that follows a pseudorandom bit sequence, I believe they would argue that a quantum process (like human thought) produced the seed. Indeed, they argue that our uncertainty about the n-th digit of pi is quantum uncertainty because if you want to bet on the n-th digit of pi, you have to randomly choose n somehow.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.