No, super admins do not have this permission. Super admins only have administrative permissions (where granted) in the ACP, they do not have front end moderator (or other) permissions unless they have been specifically granted to them. I have a super admin login that has full permissions in the ACP but on the forums they have no permissions apart from those in the Registered user group. If I grant them full forum permissions they have the hard delete capability but as soon as I remove those 2 permissions (and just those 2 permissions), the hard delete capability has gone (something I just double checked).
I note that you have only checked the hard delete post permission. You also need to check the hard delete thread permission too.
Have you checked the node permissions for the nodes you appear to be able to hard delete in?
Post a screenshot of Analyse Permissions - Node Permissions for you for one of the nodes that you can hard delete in showing both Hard Delete Posts and Hard Delete Threads entries (expanded to show all values).