1. They never forced anyone to sign it; but in general it's a stupid idea to talk poorly about a former employer in public. This guy was doing a fucking AMA on reddit about his time being employed at reddit. He knew he had been fired; and he had to know the truth was going to come out.
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.