"The clubhead always leads the shaft at impact regardless of flex." FACT.
This is undeniably based in reality and should be the basis of our understanding of how flex affects launch.
"A softer flex will give you more distance at the expense of accuracy." NOT FACT.
This is already a windy-sounding claim, but I would assert that it is in fact mostly untrue. I have yet to see any evidence that shaft flex significantly affects swing speed. In theory, a softer shaft will store energy over a longer period of time and then release energy over a greater portion of the downswing, but the energy cannot be amplified. Basically the added coil adds distance to the path the clubhead travels, but as far as I have seen this doesn't translate to ball speed, (or swing speed at the moment of impact). Any distance gains from a softer flex would be realized from lighter weight and higher launch. Accuracy, however, can certainly be affected.
"A stiffer flex will result in a push and a softer flex will produce draws." FICTION.
This is a corollary to the established knowledge that the clubhead leads the shaft at impact. However, when many players test a soft shaft that they can easily overpower the result is just the opposite, a massive push. What gives? It is important to remember that the head is attached to the shaft at the heel. If the shaft is whipping through the impact zone well ahead of the wrists, the force of the shaft release will push the club face open. Only if the shaft has an unusually high torque rating relative to flex will the softer flex close the face and produce draws.
What would be key to unequivocally demonstrating any of this is quality high-speed video of a consistent golf swing as applied to a wide array of shafts with varying flex, torque, and kickpoint ratings. The purpose of me pointing this out is to hopefully assist anyone else in their experimenting with equipment to tweak ball flight. I know the usual canard about the importance of getting fitted, but for many of use we are not consistent enough to get a perfect fit in a simple one hour session. The input data for a proper fit really comes from years of practice and study.