The short answer is that the fire department can require anything they want to. The long answer has some explanation.
I live in the Twin Cities Minnesota. There are 110 Municipalities, each with their own interpretations of the NFPA Code.
I haven't heard of exactly the issue you have where you need a permit to replace a power supply, but one municipality here requires more. They require that the whole fire alarm system shall be upgraded to current code if the control panel is replaced, even with the exact same model. Think about putting mini-horns in each bedroom of each apartment. A medium size apartment building can cost more than $100K just to replace a small control panel.
Our problem is not with the National Fire Protection Association (NFPA). They're just a publishing house that produces a guidebook (NFPA72). Actually, the NFPA has no more enforcement capability than any other reference book in the library.
Our problem is with the government that makes the laws we have to obey. The fire department is a division of the local government, and the fire marshal or fire inspector is the interpreter of the law for the government. You might be able to change the fire marshal's mind, you might be able to appeal the decision to a superior, but in the end, what the fire marshal says is what goes.
I have seen many requirements enforced by some municipalities and not by others. The best I can recommend is to remember what is required by this fire department, do what they require, and go on. You have more important things to do than to fight city hall.