I have a problem in Sharepoint 2013 which is reproducible.
- Create a document library on any site.
- Create a folder in this library.
- Break inheritance on this folder and add a user that doesn't have access to anything at all, give this user read permissions
Log in as this user and try to go to the folder using the url of the folder. You will get "Access denied".
Although doing the same procedure for a file in the list (upload a file, break inheritance and add a user to be able to read this particular file) works.