This is false, because no one is obligated to agree to anything. If my preferences are such that they in some sense add up to a Dutch book, but then you actually offer me a bet (or set of bets, simultaneous or sequential) that constitute a Dutch book, you know what I can say?

"No. I decline the bet."

I don't think that this is a valid escape clause. You don't normally know that there is a bet going on. You just live your life, make small decisions every day, evaluating risks and rewards. It works just fine as long as no one is on your case. But if someone who knows of your vulnerability to Dutch booking can nudge the situations you find yourself in in the desired direction, you eventually end up back where you started, but with, say some of your money inexplicably lost. And then it happens again, and again. And you are powerless to change the situation, since the decisions still have to be made, or else you would be lying in bed all day waiting for the end (which might be what the adversary intended, anyway).