What if they only pretended to forward it to you by mistake and you /were/ supposed to see it?
As in "it would be a shame if you could never fly again".
It is clearly a threat, and most likely a bluff. But should it be brought to court, they could claim it was indeed internal communication (and that you should feel bad for reading it in the first place). There may even be an internal response saying "no you can't be put on the no-fly list", which isn't forwarded to you of course, to keep up with the masquerade.
Before you push back at your work you have to consider possible loss of work and therefore housing/medical insurance/food.
The entire US system is designed around baked in blackmail of the individual into conforming. Not surprising at all to see the airline turn the no fly list into that pressure, it's the main technique we know to motivate people in the USA.
Back when I still argued with people on reddit I was shocked to learn that normies actually believe this is a good thing. Particular example was that the fact that so much of your life is tied to your workplace and you can get fired for political activity outside of your work. This shuts down any non-mainstream discussions. They were like "yes this is exactly what we want".
When I tried to explain "ok but there were times when racism and homophobia were the mainstream, do you think people advocating for equality should've lost their jobs for their political activity" I always got in response 502 Internal Server Error.
It's not just that lawyers are expensive and court is risky. Court also takes fucking forever. Somewhere along the way, a right to a speedy trial has been lost. People have jobs they have to get back to, families they have to provide for. The plea deal is often a way out right now, with the tradeoff of having a conviction.
Even if you're 100% innocent, it's often the better financial choice to just... take a guilty plea. The end result is we can't really say, for sure, how many convictions are actually guilty people.
The calculus gets even more complicated when we consider race. If you're a large black man, are you really going to want to take the chance in trial? If you're a meek white woman, you might be more inclined.
It's Adams defending British solders, and later being very much a supporter of the concept of jury nullification. The fact that the modern court has been allowed to not only block the distribution of this information, but actively seeks to tell jurors that they HAVE to follow the law is, to be blunt, a disgrace.
https://en.wikipedia.org/wiki/Four_boxes_of_liberty
No more of this nonsense around "arbitration" being OK. Take it all to court, force it to be on the public record.