The latter is the only thing I have found to change the site at all.
In my user list under POLICY FOR WEB APPLICATION, I have:
NT AUTHORITY\LOCAL SERVICE - FULL READ
NT AUTHORITY\NETWORK SERVICE - FULL CONTROL
NT AUTHORITY\SYSTEM - FULL CONTROL
BUILTIN\USERS - FULL CONTROL
The last one is the account that impacts site function. If I remove
it or change the permissions, it affects ALL users on the site.