Public/private compensation and credentials

This Room-for-Debate installment from the Times examines whether public school teachers are overpaid in terms of both earnings and deferred compensation like retirement and health-care benefits.  A recent AEI/Heritage study counts up the data in the National Longitudinal Survey of Youth and argues that public school teachers are overpaid compared to their private sector counterparts with similar scores on the Armed Forces Qualification Test (AFQT).  One of the roundtable contributors argues that controlling for the AFQT alone isn't enough, and once you control for years of education, public school teachers appear to earn less than they should.

Wouldn't it be nice to be able to just drop a covariate whose presence generates a result that doesn't fit with the story?