@mirewitch
You may be correct about Chidori being more angry than humiliated, but I'm not sure if that makes things any better.
From my own experience, my friends would openly suspect people of being romantically involved even when they weren't, from misunderstandings much more simple than this.
Disagreements may be inevitable in any relationship, but I'm not sure we have the same definition of the word "fight." Fights may be ubiquitous in pop media, but I've known couples that can resolve their disagreements without yelling. My parents never, not once, shouted at each other. Count to ten, take a breather, remind yourself that you're on the same side and working for the same goal. It's not a black and white thing, for sure, but in terms of degrees of hostility, there are lots of better ways to handle things.
It's good at least that we can agree that Nanoha handled things poorly. I'd be much more upset if this conversation ended without finding even a little common ground.
Still, publicly embarrassing one's partner is a textbook example of emotional abuse. It may not be severe or repetitive abuse, so there's certainly room for reconciling, but it's not something that ought to be allowed to go on repeatedly. How severe it is depends a lot on the individual, and being fictional characters, I can't speak to that. I can only speak from personal experience.