Hello,
When I tick a fork on http://mysite.tld/wp-admin/edit.php?post_type=fork screen, choose 'Move to Trash' in 'Bulk Actions' drop-down and click 'Apply' - I get this message:
You are not allowed to move this item to the Trash.
Also, there's no Trash link under fork title (where we have Edit | Quick Edit, etc).