Not Catholic Legal Theory Department

So there I was on an airplane, organizing my things on an extremely packed flight right before takeoff, when what should pass down the aisle but a woman walking (or maybe being led by) a small canine -- one of those creatures more realistically classified as rodentiform.  I looked around for some sort of explanation, but only saw other gaping maws.

I came to find out later on the flight that this is an animal which serves to calm the owner's anxiety -- or, as I've since learned, an "Emotional Support Animal."  Apparently if one obtains a doctor's note, one can bring a loose animal onto an airplane packed to the gills with people because one is thereby emotionally assisted in managing the flying experience.  Knowledgeable readers, do I have this right?

If I do, it leaves me wondering how much anxiety is sufficient to get you your plane pet, and of what sort.  How bad does your anxiety need to be to compel other people to tolerate being touched or perhaps even rubbed by a foreign, hairy beast, with no possibility of moving?  And what if the animal defecates or vomits, and one has an anxiety about being trapped in a small space with nothing to breathe but re-processed, dung-scented air?  Are there limits to the sort of animal that one can bring that somehow are more restrictive than Mill's harm principle?  If you find Bengal tigers emotionally assuaging, probably that wouldn't "fly,"  but what about my frisky and oh-so-friendly yellow lab? 

And how unstable is unstable enough to obtain this privilege?  I sometimes have anxieties on planes -- not at all about the flying or the bumps, but about the other people, their personalities, and their proximity to me.  I take it this would not be good enough.