Let the fakes discredit themselves
It doesn't work that well - people have all kinds of cognitive biases and WILL confirm their preconceived notions, but martyring them is far less effective yet, it only gives ammunition to the "true believers".
The thing is, the eventual fail when too many believe lies and too many take advantage of that till it causes a collapse or revolution is kinda painful too. And it takes too long to discover which was actually fake, pretty often - false flags can run a loooong time. But trying to fix human nature via tech has a really really bad track record all its own.
Most people suffer from at least a few of these most of the time, and given human nature looking out for #1, other people take advantage of them via this. Even once you understand, it's hard to avoid.
Who watches the watchers? Even if you had a pure heart, are you qualified by knowing all truth?