Maybe someone else has more in-depth knowledge of such code requirements.
Oh here we go...
Here's a couple links from a good source on the subject (all with building code references)
The first deals with ADA requirements for elevators and when those requirements can be deviated from. The second is all about how to provide an ADA accessable means of leaving the building in an emergency.
This last one is kind of funny for most people to get their head around. It comes from how big buildings like a hotel have to be built. In short, they have to be built so that you really don't have to worry about fires. If my next door neighbor douses himself with gasoline and lights it up to protest the latest raise in ticket prices, building codes say that the fire must take no less than 45 minutes or so to spread into my room. Furthermore, the building codes specifies that the sprinkler system be able to put that fire out within 15 minutes.
In the event of a fire, they don't want people using elevators anyway. With a Hotel like Pop, with outdoor mezzanines, someone in a wheelchair would be expected to stay in their room if the fire is elsewhere and there is no smoke or exit their room and stay on the mezzanine until the fire is put out or help arrives.
For a non-fire related evacuation emergency (zombies ... or ... meteor?) a building must either have backup power for the elevators or provide what's called 'Areas of Refuge' for mobility challenged occupants. AoR are designated places that will not block the egress of the abled (convenient for us abled) and provides an emergency phone so they may call for assistance.
As in most cases, I suspect Disney goes overboard and provides backup power for their elevators even though it's not required but I don't know that for certain.
What I do know is that I am a person who worries about and plans for any potential emergency and knowing what I know about how hotels and apartments are built, I don't worry about fires. Once you rule fires out ... reasons you may have to bail in a hurry become pretty darn rare.