Reality is, management, by virtue of their possession of Director titles, are already often public information available to investors. Number 1.
Number 2: Nudge theory is absolutely a thing, and barring a technical reason for RTO, it is 100% a powerplay by management. I have been in on meetings where those types of measures are discussed.
Poor response by management types to laborers naming and shaming is generally a very good signal that someone was relying on worker discretion or control of the flow of information to get something past the radar.
Newsflash:
People can, and absolutely should talk. Half of being a leader or person in management is ensuring that you keep your nose clean enough that the people below you don't feel the need to speak out, and if they do, that you're ready for the fallout.
It ain't hard to do that if you're being ethical, and are equipped with real, valid reasons other than narcissistic upper management dictat to back up why the company is doing X.
If you don't have that, then maybe you need to reevaluate whether or not you want to be in that spot.