The government has no right to those documents or recordings in the first place.
The massive number of Tier 3 documents and files described in the article detail foreign and not domestic targets. These are the ones that Snowden did not reveal to his press contacts, however, he has likely provided the files to the Russians and Chinese. They are the ones that are so damaging. The Tier 3 files described contain exclusively foreign intelligence and thus certainly are not protected by U.S. laws.