Use AjaXplorer server as proxy to a remote FTP server. If the filesystem you want to browse is not locally accessible by the server and you can access it via FTP, use this driver for browsing the data. The user/password used to authenticate against the FTP server can be set in various ways, either using one credential for all users, or setting each users credentials, or even using the ftp server as the credential provider.
The plugin can be linked to the auth.ftp to transform AjaXplorer into a fully-feature generic FTP client, allowing your users to log in to any ftp server they want. See auth.ftp for more info.
If you have the right accesses, you should also consider the plugin access.sftp, that uses SSH access to browse a server. It can be an interesting solution when you are struggling with permissions problems.