Most foreign agencies would probably take a far more direct route, one they've been using for centuries, and use one of the multiple moles they surely have placed inside of these organizations.
If private American communications data finds its way into the hands of foreign intelligence organizations, does it really matter whether the database was "hacked" technically or via traditional espionage? The end result is the same.
Actually, the term hacked is more often used nowadays in social engineering cases since that is how most data breaches occur. Espionage falls firmly under social engineering.
Most foreign agencies would probably take a far more direct route, one they've been using for centuries, and use one of the multiple moles they surely have placed inside of these organizations.