Hello Ambyer and welcome :3
I don't believe that I have enough experience to answer your question, but I would still like to put my thoughts down on paper/pixels. You see, I have only ever been in 2 relationships - one with my first ever girlfriend, which is still roaring on, and the other with another lady that was attached. My "first" girlfriend is bisexual (mostly lesbian though) and has a long-term relationship with a lovely girl (which I am pleased not to be involved with!).
I guess my situation was different in that I started my second relationship knowing that we were going to be each other's "third wheel". You could say I was a certified 3rd wheel and loved it
However your relationship with this couple is different...
Without having any practical experience I would say that if the couple makes you feel as official as it gets, then it doesn't matter what random people will assume. Of course most people will think that you are the best mate - the vast majority will not take a poly relationship as a possibility. It's just not how most people think by default, whether we like it or not... You can always surprise boys hitting on you by making the situation blatantly obvious and feeling awesome as they instantly jizz in their pants
(excuse my language). Of course you'll need to be sure that the couple is OK with you being open at that level, and if they are then there is absolutely nothing to be worried about.
As far the emergency situation is concerned, we could be looking at an area where little can be done because the law is involved. My girlfriend was actually a surgeon so it's funny that you have mentioned this
she did tell me that if something were to happen to her or her husband I would be unable to get through the door because the law would not recognise me as having the right to enter. I felt awkward about this but some things in life are as such I suppose
You may find that others know of a way to solve this issue, and I would certainly be interested in hearing from anybody who believes that there is a way around it.