Ahh… ok then, that is the issue. You need to install the Link extension and configure it. You have the permissions set, but do not have Link installed.
That said, there does seem to be a bug. The edit link should not have been displayed to users which do not have permission to edit an entry. It was still caught in the code hence the you do not have permission message. I corrected the bug on your site. When I push updates to Connections and Form, you will be able to update safely as I made sure to include the fixes already.
Apologies for the trouble!