Mike, thank you for sharing your experience - however, our problem was not related to person vs group duplicity....
After deep investigation, we have found out that:
When the administrator A2 was lisetd in Full Acces Administration of Server document, the effective Access dialogue for him (A2), didn't show his group membership.
For every other analyzed user (even the other Full Access Administrator) the Effective Access dialogue showed group membership!.
Note: The Full Access mode was node enabled during this observation....
Really strange, but reproducible (at least at our Domino system) :-)