Milestone: I agree with you...if the aforementioned re-exam was inter partes a third party can be involved during the re-exam and can enter objections as well as ask for a cancellation of the re-exam.
Ours on the other hand was ex parte...basically meaning "hands off'. Once it's in the PTO 's hands and the examiner is assigned along with a re-exam number it is up to them to finish the task with no outside interference from any third party. It's just between the examiner and the patent holder then to answer all questions via non-final action postings along with discussions between the lawyers and the examiner...at least that's how I understand it.
Corrections welcomed.