I have done "attends" in the UK but in order to do this I needed to be trained and accredited even to be allowed into the meeting to observe and not as some one with the power to make decisions!
The manager isn't present during the employee's presentation either though, and I'd imagine it would devolve into a circus if both parties are present during both presentations and able to interrupt/rebut directly. (Might also not be beneficial to 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.
The article clearly doesn't go into the process beyond what's on surface. When I participated both the manager and the employee wrote an initial document that would be shared with each other. These documents are the basis for the presentation. The employee had time to go through the manager's document and rebut each of the points their turn (as did the manager), so it seems slightly disingenuous to suggest that neither party has access to the other's claims.
During each parties presentation, they would go through the document and bring in supplemental evidence (which the other doesn't have access to).
The format I went in was: Employee presents their document -> Employee rebuts manager's document / Q&A -> Manager presents their document -> Manager rebuts other presentation / Q&A
The panel then has the option to bring back the employee for additional questions.
I'd be interested if/how the ordering of the presentations affected the panel.