If your files are available on another site in the grid, let's say CERN or GridKa, you can access them via grid protocols as gridftp or xrootd over the internet/WAN.
If you start 1000s of jobs on the NAF and each reads a file over WAN there is the good chance, that you will
- saturate the in/outgoing network connection to the internet
- overload the remote storage
→ you will cause a distributed denial of service attack on shared resources.
And as a result numerous local and remote network admins will try to track you down to stop you.
Advice: if you plan to access file on remote storage elements, use the file transport infrastructure of your experiment to copy these files to your local scratch space in an organized way.