If these were real grievance hearings, both parties would be able to be present during each other's presentation, cross-examine witnesses, and present (and/or challenge) evidence used to make a decision on what to do with the employee.

Could it become a circus? Yes, if procedural ground rules are not well-defined and enforced by the moderator of these sessions. One of these should be the obvious "don't interrupt each other while one side is speaking".

I know these aren't supposed to be formal legal proceedings by design, but if the parties cannot question each other -- or even hear what the other has to say! -- then there seems to be a strict upper bound to the degree of "truth" that a jury could uncover during this process.

EDIT: I didn't notice your disclaimer when I wrote this; I absolutely did not mean to give off the impression that you or your colleagues @ Amazon didn't take your responsibilities as appeal committee members seriously or didn't do your job properly. Hopefully you didn't take it that way, but re-reading this thread made me want to clarify.