I'm pretty certain that Rosamond Gifford Zoo still has a dog living in its elephant barn. Reading the AZA accreditation standards, I see nothing to indicate that housing a dog in an elephant barn is a violation of AZA policy.
Why are you so certain of this? Do you have any specific historical instances or quotes from AZA accreditation standards to back up this assertion?
Saying they'd need to "get rid of the dog" is completely ridiculous too, because even if there is something saying the zoo can't have a dog in its elephant barn (which I don't think there is), there is certainly no AZA standard banning zoos from housing dogs altogether, so they could easily move the dog to elsewhere in the zoo if they wanted.