Under the hood, GetAuthorizationGroups actually uses the Windows Authz APIs to get the user's group membership instead of doing an LDAP query for tokenGroups. The API in question uses RPC instead of LDAP, although it DOES actually end up reading tokenGroupsGlobalAndUniversal out of the directory (needs the same permissions that you would need via LDAP).
My guess is that there probably is a fix that could be done for the error you are experiencing, but it would need to be factored in to the AccountManagement API itself. The first thing would be to try to make sure they understand the problem and can reproduce it. After that, you might be able to get a patch. As to whether that would be practical for you to use from a deployment standpoint would be up to you.
I've seen a number of other people report issues with this API as well for different reasons, so it looks as if it could use some additional tuning and testing in other environments than what the testers originally applied to it. I still like the idea, but it is clearly somewhat fragile and hard to recommend as a result.