The appeal says the city never put their concerns in writing, and therefore the owner has made their best attempt to state the city's side of the case based on what they've been verbally told.
If I were to try and state the city's motivations, there is an inherent nervousness about putting people who are incapable of self-preservation (due to memory loss) in an old building that does not meet today's code standards.
The owner is arguing that in this case, the historic building code IS today's code standards, and that sprinklering the building is an acceptable level of mitigation of risk in a historic building.
As we all know, there is no such thing as a 100% risk-free building. There is only what we as a society have deemed acceptable levels of risks and trade-offs for other benefits, such as historic preservation and adaptive re-use. The owner is stating (1) they have a prescriptive right per the historic building code, and (2) their proposed safety measures also have a performative mitigation effect.