Parts of this are interesting, but the study as a whole seems fundamentally flawed. They're using real information which is already available, which means they have no control over the existing exposure and predisposition of their subjects to it. For example in this experiment:

There was one other example – tax cuts increase revenue. This has been a subject of some contention. And, again, the researchers, Brendan Nyhan and Jason Reifler, brought in both conservatives and liberals and told them about this claim of the Bush Administration, and then provided them a refutation by several economists, including several who worked for the Bush Administration, both current and past officials.

Here their refutation is the testimony of "several economists". So we're talking about a couple of specific individual people who are saying that the original statement was incorrect. It's entirely possible that those economists are shifty looking, untrustworthy, or just not very convincing. Or they could be public figures that the test subjects are already familiar with and inclined to disbelieve. In other words, the fact that their support for a position takes away that position's credibility does not necessarily speak about an aspect of human nature since it could just as easily speak about the specific impressions the economists left on the subjects.

Seems to me that in order to get any kind of meaningful data out of a study like this you would have to use completely manufactured information that can't be influenced by things people already believe.

P.S. Great thumb.