...among those who answered the survey.

This is a survey by the NHES, a government organization - do you think there is some reason for selection bias?

Here is the survey's remark on their estimation methodology:

"When applied to survey data, weights allow for the generation of national estimates from a sample of respondents. They also adjust for characteristics of the survey design, nonresponse, and noncoverage. However, biases may exist in the data if weighting procedures have not adequately adjusted for these issues. A large-scale bias study was conducted in conjunction with the 2007 data collection. Readers interested in the findings of the bias study, as well as detailed information on NHES survey methods, weighting, and response rates, can refer to the Data File User’s Manuals published online at http://nces.ed.gov/nhes ."

I think that the fact that the survey was conducted by a government organization and that the targets of the survey were families who had decided not to participate in government-run education, for one reason or another, makes a certain selection bias seem likely.

I'd expect a measure of homeschooling families to want nothing to do with the federal department of education.