A friend of mine, when asked to implement an AVL tree, actually asked an interviewer when the last time he had to implement an AVL tree on the job was. He wasn't hired.
The department should run the interviews through their own employees first. If some questions cause an "interview anti-loop" (a set of other employees S who would not hire E) it's time to revise those questions.
Revise and rehearse these practice interviews within the department, and do it blind, until all of S are willing to "hire" each other for their respective roles.
Most of the time you see the resume a few days before. They may say a few things "don't say this don't say that". (hr)
Most companies take the rejection as a point of pride. "We've rejected 100s of candidates."
I don't like the structure, I think it's very flawed, but asking you to do something you do regularly defeats the purpose.