Ah, but that requires there being officials who do know what holy magic does. Like this is ironically a real problem in real world as well. Let's take ye olde Polish dictionary for example. In old Polish dictionary, a horse is defined "everyone knows what a horse is", and dragon as "it is hard to overcome, yet one shall try." Very fucking unhelpful.I guess you're right about the crown prince keeping himself hidden about this. And I do see your point. But in this case, a holy magic user would be really easy to prove. Just have the person do holy magic in front of officials that actually know what holy magic does. It would be like someone proving they could shoot fireballs. All they would have to do is simply shoot a fireball in front of people for it to be true.
Also again, Plato's definition of man is "a hairless bipedal creature", hence Diomedes mocked him by presenting a naked chicken as Plato's "man". Just because something fulfills the definition of X, doesn't mean it is actually X. The first chapter said Fine is the only person who can wield holy magic in the whole kingdom after a long ass time. This implies any knowledge about holy magic is limited to records and legends, or maybe Fine is the first person that can use holy magic, with Elses being the one who made up the label of "holy magic". But my point is that there is enough semantic loophole for the noble brats to challenge and outright refuse Fine's magic being defined as "holy magic".