I have never had this issue! I've had both Philadelphia and Elmwood Park memberships and both accept the other, and they're ~15 miles apart. ZooAmerica takes both, Lehigh Valley does, Maryland, etc.
Just looked at the list and found this on the bottom of the page:
"In addition, participating institutions located in close geographic proximity to each other are not required to offer free or discounted admission to each other’s members in order to participate in AZA’s Reciprocal Admissions Program; for instance—Milwaukee County Zoo does not reciprocate with Henry Vilas Zoo, Lincoln Park Zoo, NEW Zoo & Adventure Park or Racine Zoo."
Maybe they're the only ones that do this? Seems like it goes against the entire idea of reciprocity, imo.