One employer that I worked for stated in the ethics manual that employees would not post or say things that were detrimental to the organization. If one did so, it could be reason for termination. Based on that, if the employee agreed to this (annually in a written statement) then there was the rule.

Anyone can hire or fire anyone he wants at any time. If he is breaking a contract, there are consequences.

No way!!! If the company can not take criticism then if should man up and fix the problem so there's no criticism from employee's