AZA facilities actually enjoy some exemptions from the MBTA - for example, an AZA institution does not require MBTA paperwork to send a bird to another AZA facility (there's an entire crazy flow chart about what permits you need for moving birds between rehabbers, exempt facilities, non-exempt facilities, etc). One of the trickier challenges in sourcing wild-born shorebirds is getting them from rehabbers in the first place. It comes down to the individual rehabber's philosophy, and I've heard of some which have opted to have birds euthanized when they are deemed non-releasable rather than place them in zoos or aquariums.