I actually don't find anything strange about that. I am reasonably well-educated and know a lot of things, and I have no idea who the US supreme court chief justice is (though if I needed to know, it would take me about 2 seconds).
The problem is that there's no reasonable way to grade the quoted rejects as false. If you aren't a lawyer (Edit: but maybe if you are*), there's really nothing about labeling John Roberts as Chief Justice of the Supreme Court that is more useful than labeling him as "the justice in charge of the Supreme Court." The error is roughly on par with asking "what does 2+3 =" and accepting "V" but rejecting "IIIII"
In short, I have dramatically adjusted downward my belief the reliability of public-ignorance surveys.
On refl...
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.