In my experience, conspiracy theorists don't have a lot of interest in these. Unprovable conspiracy theories are more interesting because it affirms their sense of paranoia, identity, feeling special, entitlement to the truth.
Conspiracy theorists might go on and on about JFK or 9/11 or Pizzagate, but how often do you hear the conspiracy type obsess about Jan. 6, an actual proven conspiracy to overthrow the government of the United States? The "proven" conspiracy theories they do care about, like MKUltra, are generally cast as far more consequential than most people would say they actually are.
That is technically an example, but I think it also proves OP's point. Faced with a clear, public, and well-understood conspiracy, the theorists can't accept the demonstrated facts. For the surface truth to be the actual truth is intensely unsatisfying and disempowering. There must be something more and deeper to it, always.
Conspiracy theorists might go on and on about JFK or 9/11 or Pizzagate, but how often do you hear the conspiracy type obsess about Jan. 6, an actual proven conspiracy to overthrow the government of the United States? The "proven" conspiracy theories they do care about, like MKUltra, are generally cast as far more consequential than most people would say they actually are.