Sometimes I wonder about the mental capacity of these union leaders. What if a off duty nurse didn't preform CPR on a guy because she was off duty?
That would be a little different, since CPR can be performed without having a specific job and can be performed by ordinary citizens. (Whereas with arrests, the police are granted special powers, authority, and protections, whereas an ordinary citizen can only make a so-called "citizen's arrest under limited circumstances and are held to the strict-liability principle) As for the union itself, the union is claiming that the police chief's actions violated the labor agreement they have with the police department. Now, whether or not that is technically true under their agreement, this is still a stupid complaint, but the union might "technically" have a point.
@predatorX, no, you wouldn't be arrested. The union's complaint is that the police chief violated the labor agreement between the bargaining units (members of union within the police force) and the police department by performing work that they claim the agreement reserves for the bargaining workers. As a civilian, your not entitled to perform police work in the first place, and even if you subdue someone attacking you the fact is your not performing police work but committing actions which are normally illegal under the criminal code but are contextually allowable according to various aspects of the legal code and common-law of your locale.