Drupal 7 problem: Content edit tab doesn't appear for user editor

In Drupal 7, there is a *very tricky* problem you might fall upon at some point. We did and because it's not *really* a Drupal bug (although it could be considered as a usability bug), it's worth writing down. The problem is simple: one admin (Joe) and two editors (Sam and Max) edit a website. They all create their own content of the type "artist". They all have permissions to "Create artist", "Edit own artist", "Edit all artist" and "Delete artist". Also, the "artist" content type has a text body which can use the "Pure text" format, the "Filtered HTML" format and the "Full HTML".