I have set the Seblod form with permissions to allow registered users to create, edit and edit own but they still cannot do this. When I log into the site as a superuser I have the edit button above the article so it doesn't appear to be anything to do with the template.
Edit button should be available if edit.own is set for group regardless of which group it is. Only thing I can think of is different calculation of permissions in Joomla and Seblod (Joomla uses category permissions, Seblod doesn't) you try adding Seblod native button if you use Joomla one. Or allow edit.own on category too.