It's rude to run through a crowded theater because you're in a hurry to leave. It isn't rude if you're making an emergency run to the bathroom. We all very clearly and intuitively understand this distinction.
By the way, the whole point of politeness is that it requires these kinds of judgements and therefore resists strict rule-making. Ideally, we wouldn't need to make a rule about dogs on planes, because nervous flyers would feel individual shame at the idea of inconveniencing other people for their own personal benefit.
I couldn't possibly bring my dog on a plane, not because of any rule, but because I'd be embarrassed and extremely uncomfortable about my own behavior. It would ultimately result in a worse experience for me, for those reasons. I'd be a self-conscious wreck.
I don't like this principle (or maybe I don't like politeness). By this principle, if I were a slave, it would be impolite to advocate for my freedom. That's an avoidable behavior; I can just keep working without pay. By this principle, if I were paralyzed, it would be impolite to ask people to have ramps and elevators. That's an avoidable behavior; it would be preferable to stay at home and wait to die. (Asking for ADA compliance is a huge disturbance!)
The obvious rebuttal is "Well, those cases don't count because being a slave or being paralyzed is a fundamental unfairness and you can advocate to resolve or work around that," but the entire question is whether people who claim to need emotional support animals genuinely are in the same position or not, whether the emotional state they need support for is also a fundamental unfairness compare to the rest of us who don't claim to need such animals.
So I don't think that the clarified principle actually helps us figure out what the right thing to do is; it just rephrases the question.