Well from the lawyers' point of view, it is their job to have the church acquitted of wrongdoing.
I don't believe that a priest stops being a priest when "off duty" any more than a police officer stops being a police officer. But by the same token I recognize that if a police officer goes home, gets drunk, and beats their spouse, you can't charge the local precinct with any wrongdoing since the crime was not carried out as a function of the police's law enforcement efforts and duties. They aren't responsible for the actions of employees who aren't "on the clock".
Arguably the key is what you mean by saying a priest "stops being a priest" or a police officer "stops being a police officer". Certainly in a general sense they don't - they retain their profession, even while not actively engaged in it.
But in a more narrow sense, that of carrying out the functions and duties of an office, it can easily be said that a person "stops" being a cop as soon as they clock out. They are no longer acting withing the authority of their office when off duty - they are effectively an ordinary citizen until they officially return to work. They no longer possess the authority or status of their office during this time.
The same logically could apply to priests. They are filling an office, and while active in that office they are invested by an external authority with the powers and duties dictated by the office. When they cease operating in the capacities of that office, they are no longer priests - they return to "lay status". Just as a police officer cannot arrest someone without being "on the clock", a priest cannot marry someone or take confession except in the appropriate places and circumstances.
The only real difference is where the authority for these offices comes from. With police, they are empowered by the legislature and the government. With priests, they are empowered by The Church.
Who decides when a police officer has their powers, and when they don't? The legislature and the government. Who decides when a priest has their powers, and when they don't? The Church.
So legally speaking, the point of this argument seems to be that The Church is clarifying for the court when a priest is considered "on duty", and when they are not. With police, there is a system in place where you have to "clock in" and anything that happens "on the clock" is something the precinct can be held accountable for. The Church doesn't use such a system, and they don't keep such records. Consequently there needs to be another determining factor.
Clearly a priest is on duty when they are performing their priestly duties - marrying people, delivering Mass, taking Confession, et cetera. But what about when they're not at the physical location of the church? What if they are not taking part of a church function? Are they on duty in the middle of the night while they sleep? Or at the breakfast table? Or anywhere outside of the church and it's functions?