You're right, because public school districts really are government entities, just like cities and townships are. They hold elections, and they have the power to tax. The confusion on this thread occurs when folks claim that schools are part of the federal government.
That is simply not true. No official in Washington DC has the power to appoint any school official. That is all done locally.
But DC has the power to seduce school districts. The feds offer money, with many strings attached. Take the money, as most districts do, and the district becomes a puppet of DC.
As a side note, I'm old enough to remember prayers in public schools. My elementary school teachers lead us in prayer every day before lunch. It was nondenominational, and the right thing to do. A big part of America died when that was outlawed.
I’ve been long aware of the distinction between what the federal government is and what public schools are, but didn’t mean to confuse you. I should have used something like “affiliated with” instead of “part of.” In places like a court of law, it’s necessary to be picky about language. But on a forum like this such pickiness could be mistaken for concrete thinking.
The government’s “power” to engage in moral corruption is well known, although this doesn’t speak to whether such behavior is justified.