I had the same skepticism as you, but the study authors did attempt to be fair by letting a set of politically balanced laypeople (equal number Democrat and Republican) adjudicate the trustworthiness of sites. They also had journalists rate the sites, but they present the results of both results (layperson-rated and journalist-rated).

I wish they had included the list so we could see for ourselves. It's still possible that there are flaws in the study. But the it appears to take the concern of fairness more seriously than most.