My submissions didn't address the Public Appointments Commission, but perhaps I do have some experience that would be relevant.
Prior to getting my law degree, I did work as a staff representative with the Public Service Alliance of Canada. The Public Service Commission, at least as it then was, was viewed as an arm of the employer in making appointments. Given my experience years ago, I would say that the public would not see this entity--unless it has changed--as being at arm's length from government and as being able to safeguard the public appointments neutrality.