This Language Log post gives a much better idea of what's going on. 28% was the number for "more than one" of the constitutional freedoms, which was later commonly misquoted as "one or more". And, of course, there's the matter of picking out a point of the distribution which is the most striking.
In other words: nobody is actually lying about the survey results. Instead, the falsehood is distributed along the chain: the press release states the results in a deliberately misleading way, and subsequent reports on it simply aren't careful to avoid being misled.
The post you linked to argues that the poll and its original press release were deliberately designed to spin results and encourage misunderstanding, and that the error in subsequent reports was a deliberate goal on the part of the pollsters.
Deliberate spinning of statistics isn't different from lying in method or result; the only difference is that they cover themselves by making sure their words are literally true.
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.