>you also can't tell employees not to say those things or you'll see headlines like the posted article and have the government claiming at trial that you're trying to hide evidence. This feels kind of odd and kind of unfair.

The point is to not do anti-competitive things. Doing them and not talking about them isn't better than doing them and talking about them. Clearly it's worse because you know you're doing something wrong and trying to get away with it.