Forcing employees to sign a non-disparagement agreement? -- Screw that. (Edit: force, compel, persuade, strongly hint: semantics.) Saying that a former employee violating a non-disparagement agreement means that it's now a good idea for the company to take use an eye-for-an-eye policy in return? -- What. No (American) non-executive employees should ever be forced to sign anything. I never have for any job. Employers…
2. That's not what he said. The former employee speculated that he was laid off in retaliation for something or other; and the company replied with the actual reason for his termination in its own defense.
In general, if you were laid off or fired from a job, it's best not to spout off about it in public (especially on the site that used to employ you). It doesn't matter whether you signed anything or not; unless your former employer was doing something illegal and you're blowing the whistle, it's best to keep your mouth shut.