Snowden was low-level, but he was basically an admin doing migration to a new system. His job description required the access he was given.
Additionally, one of the lessons learned from the 9/11 attacks was that keeping data too "Need to Know" might prevent people who actually need to know information from knowing about it.
Additionally, one of the lessons learned from the 9/11 attacks was that keeping data too "Need to Know" might prevent people who actually need to know information from knowing about it.