I won't deny that they take things out of context sometimes. I've seen it a few times, but part of the problem is that context is often difficult to identify. For the most part, I think politifact errs on the side of giving false ratings and taking statements too literally (that's just my assessment). As for the study.....I'm not sure about it. Once again, its just a simple count with no statistical analysis. I imagine a lot of the reason for their findings is just the political context, meaning there is going to be more Republican criticism during Democratic control, and the criticisms are more likely to get covered and be false.
Just a hypothesis, but I imagine you would get similar results that showed more false ratings for Democrats if politifact is around when Republicans have control of the government. I think there is definitely a selection bias, but I think it's more along the lines of finding false/misleading statements rather than a partisan bias. It's just that the out-party has more incentive to go negative, especially under unified control, when the out-party is more removed from the legislative process.
Except... Republicans ave had control of the government since Politifact's been around. Presidency no... but congress?
Outside which, the blog tends to go out of it's way to point out examples where they specifically do treat similar cases differently... which tends to be how politifact operates. They tend to give one party the benefit of the doubt, while being hyper literal with the other party... in specific sentences when not looking at the whole context of the speach.
Like it points out... a lot of this generally happens because they have no real methodological method in their research process. They give one side the benefit of doubt and look further in their context... because they're paying more attention to one side naturally.