Securing PDF documents stored in WordPress Media Library

I am using the free Simple Membership plugin. I am successfully securing pages according to membership roles (let’s call the role “board member”). The pages that a board member can see include links to PDF documents that have been uploaded and stored in the Media Library. When I attempt to edit any of these PDF documents in the Media Library I see the Simple Membership choices for (a) “Do you want to protect this content?” and (b) “Select the membership …” – which in my case is Board Member. However, if I copy the file URL for this document, open a new browser window, and paste in this URL it will show me the document. In other words, these documents in the Media Library are visible to anyone on the outside if they can determine the URL. Although this is a de minimis security risk the functionality is not behaving as I would expect. I could not find anything discussing this in prior forum posts. I would appreciate any guidance here. Thank you.