We have an apparently ambiguous word: "probability". That we accept it's ambiguous (the thesis of this post), means that there are situations where either of its multiple possibly contradictory meanings is intended. This doesn't negate a possibility of there being a concept that can be applied to most situations, doesn't itself suffer from ambiguity, and is usually referred to using the same word.

There is no apparent contradiction here: the disagreement you point out results from equivocating between the ambiguous word "probability" and (presumably) the more specific concept of probability that Jaynes refers to.