Ah, the next to last link you provided gives us useful additional information. The October 2010 data was derived from 54,000 households, and extrapolated out to 293 million people, of whom about 91 million were ages 3-25. If you figure 2 kids in that age range per household, 100,000 actual kids get projected onto 90 million total kids. Each kid surveyed equates to 900 projected kids. So it only takes a couple of wrong answers to get a number on the chart. (Alternatively, it only takes a couple of extreme outliers to generate "accurate" data that isn't properly representative of the population.)

There were 7,000 projected 15yo first year grad students from the October 2010 data. But in October 2009, the most-advanced 14yos were only in 11th grade - and there were 12,000 of them. So unless half the 14yo 11th graders skip senior year and the entirety of college, and go straight to grad school, then yes, I think there are a non-trivial number of people who misunderstand the form (or for whom the interviewer records the wrong answer).

There were 14,000 projected 16yo first and second year grad students in October 2010. But in October 2009, there were only 15,000 15yo first-year college students (and no 15yos with higher standing).

As another data point, in 2009, there were 342,000 black grad students in the US, according to the Department of Education. (http://thefreshxpress.com/2011/06/new-african-american-graduate-enrollment-statistics-released/) The Census data reports 479,000 black grad students - 0.8% (4,000) of whom were 15 years old, and none of whom were 16-19. (It looks to me from the tables by race that white people misrepresent grad school status at higher rates, but I couldn't find a second source of that population size online - and I really think that if anyone believed 1% of black grad students were 15 years old, it would be all over the press. Particularly when a 15yo college graduate of any race tends to attract some press.)

My guess as to the misunderstanding is "first year of graduate school vs first year of high school."

Likewise, my guess as to many of the "wow, look at all the kids who double-skip" is a misunderstanding of "grade in school" vs "years in school."

I also suspect that there aren't really 10,000 40-somethings actively enrolled in 6th grade. (As opposed to "dropped out of school in or after 6th grade.")