No, if the coins are independent, the Bayesian is not fooled even when seeing only that coin. The argument was in my post above.
The inference in Bayes only depends on the data, and the flips of other coins doesn't make a difference if independent. Frequentist testing can depend on things like stopping rules and hypothesis tested, which aren't correlated to the actual truth and therefore should have zero effect on inference.
They can cherry pick and only show some flips of that coin, but then they really need to be outright lying or you'll ask why only some flips were reported.
The inference in Bayes only depends on the data, and the flips of other coins doesn't make a difference if independent. Frequentist testing can depend on things like stopping rules and hypothesis tested, which aren't correlated to the actual truth and therefore should have zero effect on inference.
They can cherry pick and only show some flips of that coin, but then they really need to be outright lying or you'll ask why only some flips were reported.