Well, let's take the opposite of the argument: is it impossible to keep anything secret if lots of people must keep it secret?
Are the plans for a minuteman ICBM missile readily available and acknowledged? After all, tens of thousands of people designed them, maintain them, manufacture them, and conceal them. Certainly someone has mentioned exactly how they work, what signal frequencies their computers use, and how to build one yourself? If not, then it isn't happening.
How about a space shuttle? That's not secret, right? Oh? It's classified? Well, too many people worked on it. But, I don't see anyone revealing how to build it? It must have never existed at all, then.
These threads pop up time and time again, their basis is always fundamentally flawed. The thought process of "certainly if so many people are keeping a secret, at least one would say something!" Furthermore, if they do say something, would you believe them? How many whistleblowers out there have tried to revealed critical failures in government only to be forgotten, ignored, exiled or executed? The world is filled with many secrets, the larger they are, the more implausible the truth becomes.
After all, you might even have whistleblowers here. People who understand it is faked but without the wherewithal to reveal themselves.