I had the same issue with SQL Server 2014 (Management Studio could not see the folder in which the backup file resided, when attempting to locate it for a Restore operation). This thread held the answer that solved my problem. Quote:
The SQL Server service account can be found by Start->Control Panel->Administrative Tools->Services. Double-click on the SQL Server service->Log On tab. You'll either be using the "Local System account" or "This account" to define a specific account. If you are using the Local System account, you won't be able to reference backups that are not local to the server. If, instead, you have defined the account to use, this is the account that needs to have access to the backup file location. Your ability to access the backups using your personal logon is irrelevant; it is the SQL Server account that is used, even though you are initiating the backup. Your IT people should be able to determine what rights are granted to each account.
Hope that helps someone.