Okay so The Anonymous user group are also full users.
In that case you need to create a Group for your non anonymous users.
Trust Levels are shared among all members where as custom groups are a list of members only
Category Setting
Security
- +Anonymous Grp See
- (del)Everyone See/create/reply
- +NonAnon Grp See/create/reply
Also delete setting if you used a “trust_level_#” group. If the member is part of any group that can create/reply they will have ability to do so even if part of group(s) that do not have the per.issions