I had this thought too a bit ago, and flailed about a bit trying to make it rigorous. I've thought about it off and on since then. Here's a sketch of what I've got:

Part 1: Suppose we have an entity who acts to maximize her own current credence in various positive outcomes. She will behave identically to a VNM-rational entity trying to maximize the probability of those outcomes iff she is VNM-rational and her utility function is U(P(outcome)=p) = k*p for all p and some constant k.

Part 2: Any credence-maximizer wants its future selves to be probability-maximizers, since this maximizes its current credence in future positive outcomes. Therefore, an entity that pre-commits to act as a probability-maximizer, or equivalently as though it had a linear utility-of-credence function, increases its current utility, at the possible expense of its future selves' utilities. Therefore any credence-maximizer that is capable of pre-commitment or self-modification will act identically to a VNM-rational probability maximizer.