It would take some serious econometric analysis to answer the question definitively, but my knee-jerk reaction is "nonsense." If comparing college-educated public workers to uneducated private workers is apples and oranges, then comparing college educated teachers to college educated engineers is apples and kumquats.
About half the public workers at the state and local level are teachers. Teaching requires a college degree, most private jobs don't, and so it's clear that public workers will be better educated on average than private workers.
Unfortunately, a college degree isn't by itself a good measure of education. Different majors attract students with different academic abilities. People who can do chemical engineering don't typically get education degrees. They know that chemical engineers make more, and the discipline is more intellectually challenging. The best students go into engineering, medicine, finance and the like, not education and sociology.
I've known many fine teachers, some of them with fine minds and able to do well in any discipline they choose. The performance of teachers on tests like Texas' TExES/ExCET don't create confidence that the fine teachers are the norm, though. There are way too many tenured time servers in our school systems who have the intellectual skills of a hamster and much less intellectual curiosity. They aren't underpaid.
Educational administration is another place where there are too many people making too much money. The ranks of administrators should be ruthlessly culled, the money saved put into the pockets of classroom teachers (after we've done a bit of culling there, too).