Nevermind. I had it in mind that un-dutch-bookability was a property of perfect Bayesianism alone - so that in the way that all other methods are approximations of Bayes, plus or minus some constant, or restricted in some way, these departures from Bayes would open up non-Bayes systems to some incorrect calculation of probabilities, and so it would be possible to set up a situation where their calculation departs from Bayes in a systematic way, and then set up a Dutch book diachronically. It seems like you might be able to do this for frequentism, but it turns out that there are other, non-Bayes systems that are immune to Dutch books as well.