To me it's not purely a question of numbers. A leak-less intelligence apparatus could exist if the only members were radically different in terms of culture than the rest of the population. People who went to special schools and who at a young age were identified by themselves and/or family members for military/intelligence careers. To me people who go to West Point and the Citadel are not "regular people". They may be fine people, but culturally they are not the same and may have a different set of values.
However after 9-11, the intelligence apparatus grew so large that it pulled in a lot of ordinary nonmilitary people, some of whom were not raised to unquestioningly follow orders that they perceived to be unconstitutional/immoral/etc resulting in folks like Snowden. So in that sense it is a question of numbers to fill high growth. We may have a movement on or hands but maybe not-
I think it is possible to have a leakless surveillance state with a military intelligence minority "keeping check" on a non-military freedom-loving-but-freedom-denied majority. People "selected" to work in intelligence would just hve to be people "built inside the system", going to military academies etc from a young age. Just one frightening distopian thought to wake me up if my 2nd cup of tea doesn't work.
That being said, I don't have any real-world knowledge or experience in the real cloak and dagger world of intelligence and national security, so anything I say is uninformed speculation.