It is impossible to keep news of possible disciplinary actions a secret. Prior to taking disciplinary action there will always be verbal warnings, remedial actions, written warnings and so forth. Other employees will notice this and will also note the response of the employee(s) in questions. In many, if not all, of the instances the employee(s) will discuss this with colleagues and friends in the workplace.
It is even more certain that the supervisor/manager of the employee(s) in question would have discussed the matter with other supervisors/managers and higher positions seeking their advice and guidance on how to handle the matter.
When a person from within the business chairs the enquiry, he or she is will be (most of the time) be informed by a senior person what the outcome that the employer desires must be.
How then will it be possible to choose an impartial and unbiased chairperson from within the workplace, and how will the chairperson then be free to apply his mind as opposed to apply the pre-decided outcome desired by the employer.
If this is the case, the chairperson is simply going through the motions and following the instructions regarding the desired outcome, and the proceedings become nothing else but window dressing.