Yeah, but they could make it actually part of the curriculum, but that would likely backfire.
An anecdote, my kid was with his friends and one of them asked "How do bad guys get guns?" and one of the other kids said "They buy them at the store" and I just about had an aneurysm before I could find out where he learned that (his teacher, in an attempt to lump lawful gun buyers in with criminals).
The problem is that it is already in the curriculum in so many ways (as you discovered).
They have been writing history and civics textbooks with the stated purpose of spreading the idea of "government as a force of good" for 40+ years. They have re-written the history of the civil rights movement, the civil war, Lincoln, even the revolutionary war to sanitize monarchism and central, command economies and transfer all of their profound sins to "them".
Not specifically with an anti-gun message, but something far worse.
A claim that government is a benevolent, paternal figure that we should trust. That way when it says we should ban guns, drugs, booze, transfats, super-size, pizza, smoking, free-speech, Judaism, etc... People believe their benevolent, paternal overlord.
It is an anti-self-determinism message that far eclipses guns in its damage to kids' (and the adults they become) psyche and understanding of their rightful place in the world as free people, presumed innocent until proven guilty and free to make their own choices - good AND bad so long as they do not hurt anyone else.
On that last part of "hurt anyone else", the insidiousness of their message manifests in the claim that the "cost to taxpayers" is sufficient "harm to others" to regulate behavior. Of course the cost for bad decisions is not borne by tax payers without a nanny state in the first place. This is a tautological justification.
They must prevent the behavior who's cost they claim they will bear when they take your liberty in trade for false security.