Permissions in phpBB are powerful, complicated and sometimes hard to explain and one thing that gets a lot of complaints. Having said that once you understand how they work you can do anything your heart desires with them. Firstly they are stacked. A user can belong to multiple groups but its the sum of permissions that decide what they can do, for example when they first join they are automatically added to the registered users group which everyone belongs too including the admin. This group has very limited permissions by default. since an admin belongs to the admin group and will have additional permissions they override the lower settings of the limited permissions in the registered users groups. I think i understand what you're trying to do so I briefly explain how i would set it up.
You'll want to set up two groups for each forum, one for the moderators/admins and one for the users if you want to allow the moderator/admins the ability to allow access to the forum.
First set up a hidden group we'll call the "forum X admins " you can assign one person as the leader of this group. Since the group is hidden only the members of the group know it exists. The "leader(s)" can add or delete members of this group. You set the permissions of this group so that it has moderator privileges within only their forum. By adding or subtracting people from this group the "leader" by default is giving them permissions.
For the public you'd set up a second group and call it "forum X members " and assign someone as the leader(s). You could set this group as request only so they they would go into their control panel to request access to the group.
When you set the forum up you would remove or restrict the registered users group and add "forum X admins " and "forum X members ". This way only their a permisssions apply.
I know it sounds very complicated and it is BUT like I said it's quite a powerful system once you understand how it works. You can drill down permissions to individuals if you wanted.
