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.
I'd recommend you read Greenwald's book, "No Place to Hide". Snowden was not exactly "low-level", he was in training for operations. He backed down to a low-level position by choice when he wanted greater access to documents. He even took a pay cut to do so.
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.