I have been aware of this work for a while and find it really interesting and thought-provoking.
I think considering the increasing body of evidence that is indicating a link between the gut and the brain, it would be a very brave person who suggested that diet does not have any effect on either the development or progression of PD. I know in my own experience that what I eat has a significant effect on how well I feel.
I am also particularly frustrated that "reputable" journals have such a bias towards Randomized controlled Trials, most often financed by drugs companies, and fail to take into account studies with a different methodology. As we also don't have a known method for measuring PD progression I think Dr Mishley's study is a great start for trying to establish where there is a correlation between lifestyle factors and PD progression.
Personally I will do whatever I can to continue to be what she describes as a "positive deviant" ;-)