Hi Alex,
This is a problem of how Joomla! works. You can see any article by passing the parameters to the url. You must ensure the right permissions when you create a content type, not only for the form, also for the content view or list&search view.
You must have in mind always that any kind of content stored as article will be visible with this kind of url: index.php?option=com_content&view=article&id=XXXX except those who has the right permissions.
If is the public access what is worrying you, just add a hidden field in the form called "Article Access" and go to button 2 Live / Live value and add the ID of the desired level access, 2 for Registed or 3 for Special, or any level access you have in your panel.
Best regards