Also, what incentives are there for answering truthfully? The alternative explanations provided a Language Log seem better, but I used to take these sorts of results as primarily being evidence for a high natural frequency of trolls in the sample population.
I seem to recall that the usual result of studies that investigate whether research participants perform better when incentivized is negative. My best guess as to why that would be the case is that people are already surprisingly strongly motivated to do what the researcher wants them to do (remember the Milgram experiment!) I don't remember seeing any studies specifically of how incentives affect general knowledge tests; of course they could be different from other tasks researchers assign to people, but it would surprise me if that were the case.
How many times have you heard a claim from a somewhat reputable source like "only 28 percent of Americans are able to name one of the constitutional freedoms, yet 52 percent are able to name at least two Simpsons family members"?
Mark Liberman over at Language Log wrote up a post showing how even when such claims are based on actual studies, the methodology is biased to exaggerate ignorance:
If, every time you heard a claim of the form "Only X% of Americans know Y" you thought "there's something strange about that", then you get 1 rationality point. If you thought "I don't believe that", then you get 2 rationality points.