People keep talking about data, some of those people have offered anecdata.

I don't see how this question really can be answered satisfactorily with analysis. Any real life testing is going to be polluted horribly with confirmation bias. Jan Heine and his crew are going to be faster on bikes with the stiffness of a playground bouncy toy, and the people that think bikes need to be stiff are going to go faster on stiffer bikes.

And everyone seems to ignore the fact there is a hinge with very weak restoring force right in the middle of bike frames. That has got to influence the feeling of stiffness that a rider gets. This is masked quite a bit because most bikes have very similar geometry