The statement about Bayesian inference is only apparently that, and this is a very poor way to look at problems. If one does not know the state of nature, one should use a linear combination of the probabilities of the outcomes in the various states of nature, which can be considerd an integral over states of the utility given the state of nature. It is the weights given by the decision-maker to the various statss. The normalized weights act like probabilities, but it is not necessary to normalize them.
Normalization also can make approximating the optimal procedure quite difficult.
I do not claim that these views are those of the Statistics Department or of Purdue University.