What screens are we talking about? It's possible the access table is incorrect.
Check what other callings are recorded for him. Also make sure the MRN on the account he's using matches the MRN on his record. We've seen cases where someone ended up using the spouses MRN because the MRN on the Temple Recommend was swapped, or they were using the spouse's account because "it sees more".
Note that Sunday School is a part of the Ward Council, and the ward council has some very broad responsibilities for individual members. (See General Handbook 7.4) I'm not sure if that extends to 1st Counselor, but if it does, it will allow him to see a lot of membership information. Certainly more than he did as a Stake YM Presidency (who has no responsibility for individual members).
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