Is it really that odd? The point isn't that you can't say those things and you can't tell employees to not say those things. The point is that you can't do those things, and separately, you can't tell employees to not say those things.
Your characteristic made it sound like the government's end goal is for the company to simply not say those things, in which case it would be silly for them to also not allow you to tell employees to not say them. But of course the government's end goal is for the company to not do those things, and separately, they don't want the company to instruct its employees to refrain from discussing those things because that indeed looks a lot like trying to hide evidence.
Right, there's nothing odd or unfair here unless you're an anticompetitive company trying to get away with anticompetitive practices.
It's like saying that it's odd or unfair for someone to have "how to hide a dead body" in their search history as evidence against them while they're on trial for murder. But your honor, if I'm being penalized for researching how to hide the body, it's unfair because it makes it more likely that my murder will be discovered! Think of the chilling effect this will have on murderers, and the devastating economic repurcussions on manufacturers of bone saws and rubber hose!
Instructions to not _do_ things are conspicuously lacking from these trainings. We were instructed not to consider the legality of what we were doing, avoid using all the above language, and let the lawyers clean up afterwards if it's necessary. I think the only exceptions might have been export controls, copyright (loosely), and HR training (discrimination, etc.).
Yes, that's very odd. Because without such corporate policy being allowed, competitors can easily bribe some employees to loudly speak it out and use it as evidence of bad acts/intention. It's almost impossible to counter it as long as they're careful enough to hide such collusion.
You're overreacting. Corporate should have a minimal defense against these kinds of attacks in the court. One defense is "Okay, we don't speak this in our company. We made it clear by policy and if someone does at least this is evidence that it's not our company-wide strategy". Of course, whether this claim is accepted or not is up to the court, but interpreting this as a part of evidence destruction is pretty "creative" and I see this as a signal of being a weak case.
Your characteristic made it sound like the government's end goal is for the company to simply not say those things, in which case it would be silly for them to also not allow you to tell employees to not say them. But of course the government's end goal is for the company to not do those things, and separately, they don't want the company to instruct its employees to refrain from discussing those things because that indeed looks a lot like trying to hide evidence.