As copyright currently exists, what they were asking for IS the law and IS legal. Tresona was "destroyed" as you put it because they were claiming copyright defense rights for music and performances that they had no right to defend. It'd be the equivalent of me personally suing a fanfiction website for publishing Harry Potter fanfiction. Yes, it's by-the-law illegal, but JK Rowling (and/or her attorneys) has to defend it, not me as a third party. I have no standing to bring the suit, and it would be summarily dismissed.
You're also right in that there is nothing in US code that says specifically "public schools must have XXX license" however the code says "in order to perform this piece publically, you must have XXX license from the copyright holder." And it also says "in order to record a piece and distribute the recording, YYY license is required." And finally it says "In order to stream a piece on the internet, ZZZ license must be granted by the rightsholder."
We are NOT exempt from copyright law as public educators or as school bands. Fair use doesn't apply for unlimited reproduction or public performance. Fair use is VERY, VERY narrow.
When you buy a piece of music from (example) Hal Leonard, you're buying a performance license for it as well - but you are NOT buying a recording license. There is a distinct legal difference between mechanical rights and sync rights as well.
In short, nearly everything you said is a half-truth. Please listen to attorneys and copyright experts, not armchair quarterbacks. Everything I've said comes DIRECTLY from the training my district has provided regarding copyright and fair use for our music teachers.