That statement is a classic anti-homeschooling and anti-Christian talking point. But regardless of what one believes about how we arrived at the point we are on Earth, the premise of the statement is that publicly schooled students don't believe incorrect ideas, like "Young Earth Creationism".
But in reality publicly schooled students often don't even know who Charles Darwin was, and lack the reading skills to even read his writings. And they often believe all kinds of incorrect or false ideas, and lack basic knowledge of math, science, religious history, and many other things.
Many high school students and most adults can't correctly answer the question "how old is the Earth?"
Also, for just about any career except perhaps a petroleum geologist, how the Earth got formed and came to be in its current condition is unimportant. Most of us will find that our knowledge of topics like the long term history of the Earth has no effect on our daily life.
If knowledge of the history of the Earth is really that important the authors would note that publicly schooled students actually don't know either, instead of attacking some small subset of Christian parents who believe in a recently formed Earth.
+1
Also, “science” actually changes. There are hardly any respected specialists today that believe Charles Darwin’s _original_ theory, unmodified.
So why prescribe “correct” ideas instead of letting ideas compete?