It does! This is what I mentioned several times and very precisely when emphasizing the backward part of the Viterbi algorithm, but I know it's tricky (carefully look what the question is about): do not confuse what is computed with the way it is parametrized: it's not because we parametrize with that we are not maximizing .
More precisely w.r.t. that very question: if you want the formal proof in this very case: . QED
But pay attention to what is referred to: parameters, not considered altogether, I mean, not when talking about the global proba are indeed only left to right : ; but as soon as it's about the whole (global) proba, there is no "left-to-right biais" anymore, only the global proba is under consideration.
I hope it makes sense....