Is that a US think? I've worked for employers in several European countries and have never heard an employer telling me not to discuss pay. Once a manager told me not to tell everyone about a pay raise as it was out of schedule and he didn't want lengthy discussions with other employees. But that was his personal request, not a request by HR. If I had wanted to discuss it I could've done without consequences, he made that clear as well.

It's still unusual to discuss pay in many companies but not because the employer prohibits it.