Rate Form Owners has Full Control: 
![Rate Form Owners][1]
Dev User3 is part of Rate Form Owners: 
![DevUser3-names are blacked out to protect the innocent][2]
This is what they should see: 
![Should see][3] When I select "Rate Form" to open the table pulling the web part, this is what they should see: 
![Should see again][4]
BUT, when logged in as Dev User3, a member of Rate Form Owners, with Full Control of this subsite, this is what they see when they try and open the list: 
![Access Denied][5]
Here is the uniquely secured content on this subsite: 
![Uniquely Secured Content][6] Notice that the All Submissions list is not on here.
Here are the page permissions (inherited from parent): 
![Page Permissions][7]
Still other people in the list cannot see All Submissions.
(images removed)