No, you don't need to grant permissions for SQL itself. They just have to have permissions for that folder. First test.
As an local admin user, can you browse to the AC folder, make a text file, write to the text file, save it, then delete it.
Sorry for the stupid question: But do the users have share permissions or NTFS permissions. Let me know, then I will give you some more ideas. Also, try adding Authenticated Users and not just domain users. If you want to be a little less secure, you can put in "Everyone."
Is there an error code when you get the error?