Hi
There are two aspects: Permission and View Access.
Permissions are all the privileges of which User Group (UG) can do things, which in this case is Download. So set the permissions for your top level categories for the Registered UG to Allow for Download. Make sure you do not have Deny set anywhere, especially not in Public UG for any category.
View Access is who can see things. So set the top level Categories View Access to Public
Colin