Sadly that's not true. The average American, although supposedly schooled, has no idea what DNA is.
Sure they do, it's just full of negative connotations. To the average American, DNA is the stuff in blood, saliva, semen, hair, and fingernails that lets the police identify and catch criminals. And when you ask them if DNA should be in food, that's where their mind goes; of course there should be warning labels on food that might have somebody's blood or saliva in it. I would bet money that a majority of respondents to the survey assumed that "DNA" equals "human DNA."