One of the questions, put on there as a test to ensure the children understood the format, was "I eat breakfast with Martin Luther King Jr every morning." (The lesson mentioned him, among others.) They were expecting 1s, but the average answer was 2.
Perhaps the "strongly" in the "disagree strongly" gloss is being understood to require an emotional reaction? It's not a phrase I'd normally use to describe an understanding that something I don't particularly care about is factually wrong.
I may be misremembering it- 1 might have been "false," 2 "mostly false," 3 "neither true nor false," 4 "mostly true," and 5 "true." I do remember that at the time I thought it was a disastrous showing that mostly invalidated the results of their study (or should have had a far more prominent role in their data analysis).
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.