The mediator is absolutely working for the company. The whole point of this is to retain people who might still provide value to the company, with the idea that it's cheaper to retain an existing employee than to recruit and hire a new one. The process doesn't need to be "fair" from Amazon's perspective if it accomplishes this goal. The main goals for a mediator (again from Amazon's perspective) would be (a) to improve this process (retain more good employees, keep fewer bad ones) by bringing more objectivity and training to bear, and (b) mitigate potential PR downsides by reducing real and perceived conflicts of interest.
I do think a mediator could accomplish these goals. While the conflicts of interest might not be reduced to zero, it's likely that the pool of mediators will have more degrees of separation from the managers and therefore will reduce conflicts. (Whereas the normal employees that are on the jury have to consider the very real implications of their actions if they contradict what an important manager says.)
this sounds like it's ignoring political realities. if you find against the employee, they are gone; if you find for them, now there is a manager, maybe an important one, at your client who's pissed at you and might make noise about it to higher ups. better for business to do what the manager wants.
I do think a mediator could accomplish these goals. While the conflicts of interest might not be reduced to zero, it's likely that the pool of mediators will have more degrees of separation from the managers and therefore will reduce conflicts. (Whereas the normal employees that are on the jury have to consider the very real implications of their actions if they contradict what an important manager says.)