This is guidance that NALC publishes, I am not making it up. If you read further in the Regulations you mention, then these Regulations restrict access for inspection to items listed in the 1972 Local Government Act, Schedule 12A. There are strict reasons for closing meetings and these mirror the list of documents identified in Schedule 12A namely information:
1. relating to an individual
2. that can identify an individual
3. relating to the financial or business affairs of any particular person (including the authority holding that information).
4. relating to employment matters
5. relating to legal proceedings
And section 16 of the Regulations specifically refers to members of Local Authorities and not members of the public. Therefore, if the committee went into closed session for the very restricted reasons involving the above information, the councillor who is not a member would have to leave the meeting.