I'd be surprised if Amazon would give a shit if Clarkson did punch someone else
Amazon's lawyers give a huge shit about Clarkson's capacity for future violence in the workplace. Hiring someone who is known to have a propensity for physically abusing co-workers produces a huge legal liability for the employer. If he punches someone on the set of the new show, that person will sue Amazon and in court, there will be a huge claim paid by Amazon for criminal negligence.
That's really why he got fired from BBC. It's not about being PC. When he punched the first person at work, that victim could only win a suit against Clarskon. A second attack would bring the employer into liability for knowingly maintaining a dangerous workplace. If they didn't fire Clarkson at BBC and someone else punched another co-worker, the BBC could be liable because of the inaction against Clarkson sending a message to other employees that punching your co-worker is tolerated by the BBC.
I would not be surprised if Amazon's risk-management department has assigned some kind of bodyguard or conflict resolution expert(s) who are on set for each filming. Amazon is a public company and this is a typical sort of precaution that would be insisted upon by the risk management department.