Briefing employees about commercial security within an organisation, and not to broadcast any unauthorised news about that organisation in an uncontrolled manner, including the threat of punitive actions and dismissal, is a normal commercial practice.
It is sometimes emphasised to employees if there are obvious public events or occasions where the company wants to control press reporting about contentious subjects or new developments happening - where contentious can mean redundancy talks, etc. as well as discussing company/trade secrets or processes outside the premises. So 'gagging' instructions are not abnormal and are most often commercially driven.
This is why you only read of ex-employees (from waitresses to Chiefs of Staff) mouthing off about how their old company was really rubbish (and often just after getting their 'K')