It's possible that adding an interaction term for classroom quality and involved parent would show that there's zero marginal benefit to a good classroom if you're an involved parent. That result seems orthogonal to their research goal, which was estimating the mean impact of a quality classroom for the "average" child.

The phrasing, "they should control for" has a specific statistical meaning, criticizing the model as having an omitted variable problem -- that they left out a regressor that is correlated with both the dependant variable and at least one of the other regressors. That is a different criticism than suggesting an interaction term.