"it'd be a lot harder to stay secret"
No it wouldn't. There's hundreds, if not thousands, of major Government secrets that we'll never know about even in this age. Hell, if you believe in UFO's and such, just look at those, despite all the video and audio and picture evidence, there's STILL no hard proof and there's still just as many people who don't believe as there are that do. Sure, there may be a couple one-book subplots about fuzzy pictures online of a unknown person turning into an animal or something, but even then there would be a dozen commenters on that pic crying 'Photshopped!'