Hopefully I am not going crazy here, but I have removed the BUILTIN\Administrators login and explicitly added NT AUTHORITY\SYSTEM as a Login with the sysadmin role.
My SQL Server Agent service is running as localsystem.
I noticed my jobs that were owned by NT AUTHORITY\SYSTEM were failed with an error of: The owner (NT AUTHORITY\SYSTEM) of job <job name> does not have server access.
I tracked it down to the stored procedure msdb.dbo.sp_sqlagent_has_server_access which has a special case for NT AUTHORITY\SYSTEM in the code:
IF (UPPER(@login_name collate SQL_Latin1_General_CP1_CS_AS) = N'NT AUTHORITY\SYSTEM')
IF (EXISTS (SELECT *
WHERE (UPPER(loginname collate SQL_Latin1_General_CP1_CS_AS) = N'BUILTIN\ADMINISTRATORS')))
SELECT @has_server_access = hasaccess,
@is_sysadmin = sysadmin,
@actual_login_name = loginname
WHERE (UPPER(loginname collate SQL_Latin1_General_CP1_CS_AS) = N'BUILTIN\ADMINISTRATORS')