I believe that "bad-mouthing" does not imply "lying". There are no laws against vilifying, criticizing severely, speaking unfavorably of big, powerful businesses as long as you have some backup in facts.
Edit: Supreme courts (or equivalents) in most countries make it very clear in their verdicts that protecting the right to expose scoundrels is very high on their priority list. Especially if the scoundrels are big and powerful. Public interest and all that.
That's why nowadays in almost every company in the agreement the employee signs one of the terms is that he is to never talk about the company in a way that will affect it's reputation negatively.
IANAL, but it sounds like a clause like this flies directly in the face of the First Amendment to the US Constitution. I very seriously doubt that any company can control its former employee's true speech.
