Thanks again Ken for all your suggestions, unfortunately I have not progressed any further by trying them:
http://site/admin/roles/assign.php?contextid=1&roleid=1
Sorry, but you do not currently have permissions to do that (Assign roles to users)
http://site/backup/backup.php?id=2
You need to be a teacher or admin user to use this page.
In mdl_role_capabilities table, moodle/site:config and moodle/site:doanything rows, roleid is 1.
In mdl_role_assignments userid 2 has roleid 1.
No backups for courses in files under uploaddata or anywhere else.
No mysql tables reported needing repair.
All dead ends...
Looking at mdl_role_allow_assign table there are no rows for roleid 2 with allowassign 1 or 2, is this right? Not entirely sure if allowassign is referring to role 1 and 2, but notice that roleid 1, which should be guest, but for which there is no row in mdl_user table (ie. first row is userid 2), has allowassign 1 and 2 tuples.
If I can't get permissions sorted out to allow course backup I will be manually rebuilding course quizzes from question entries in database...ugh. brutal.