False, though common, misunderstanding of responsibilities. The NRO is the operator/owner of the space asset. The NSA is (one of) the customer getting data from the NRO space asset. (along with many other sources)
Though I would bet good money that a vastly greater percentage of what the NSA does for traffic interception, storage and analysis is related to terrestrial based networks (or terrestrial-to-local wireless like LTE) rather than space based, these days.