In part, yes. The PL self-regulates and can impose whatever decision it sees fit within the current rules. The Commission will reach a conclusion and either party then has the ability to appeal, where an Appeal Board would hear the appeal (the members, similarly to the Commission are selected by the Chair). Practically the definition of marking your own homework (twice!).
Judicial review is not available, so City could not challenge the procedural aspects of the case by the PL, as the PL is private body so not subject to judicial review (R v Jockey Club 1992).
City could try and commence court proceedings if they view the PL to have breached their contract with City during the course of the investigation and/or subsequent hearing.
The High Court/Court of Appeal/Supreme Court wouldn’t have the power to overturn the decision(s) made by the PL per se, but their ruling could seriously undermine the legitimacy of the PL ruling and be incredibly embarrassing.