Ok then, here we go
To start off with, if it's not a secret it doesn't need keeping really - all it needs is enough of an aura of disbelief that it gets generally ignored.
So, the people who actually work on things like that are pretty well kept (let's say).
A few here and there think they can make their fame, so take pictures or similar.
Someone else who's still loyal takes a few pictures and does a little tweaking, enough so that the internet says "that's photoshopped, I can tell by the pixels" (in the old days, the press says "that's been doctored, look at the shadows").
Enough deliberate fakes swamp any genuine ones to the point of being ignored.
Same with stories - one person saying "I played chess with an alien" is just a random mental, right?
Boom, it's a conspiracy theory. Aliens, Titanic, faked moon landings, dolphins have underwater labs experimenting on paper, flat earth...
Everybody is so wrapped up in how much charge is left on their phone or that there's not enough foam on their coffee it just gets lost in the noise.
Until or unless something explodes, nobody really cares enough - and there's so many conspiracies (all part of the plan) and everyone is so easily distracted by shiny.
Success - everyone knows the secret, just pretend it's still a secret and nobody will believe it anyway.