I think I've tracked down this extraordinary claim to this 2007 DoD paper on the "Global Information Grid", where it states:

Key target GIG technologies include: Very large scale data storage, delivery, and transmission technologies that support the need to index and retain streaming video and other information coming from the expanding array of theater airborne and other sensor networks. The target GIG supports capacities exceeding exabytes (10^18 bytes) and possibly yottabytes (10^24 bytes) of data.

So someone had a vague plan for a storage centre and couldn't put a finger on how much it would store to within 6 orders of magnitude! I don't count this as evidence that the NSA has more storage capacity than everybody else on the planet put together.

http://www.msco.mil/documents/_7_GIG%20Architectural%20Visio...