You can not easily stop employees from exercising free speech. Any such limitations have to be tied to their representing the employer and not simply preventing the employee from giving their opinions outside the job. In some way the restrictions are more of an intensive for the public to question the reasons the information is being held back.
Then there are all the whistle blower laws that would come into play; you can not prevent an employee for revealing anything that can be viewed as revealing violations of law by the employer.