Why that's just wrong!

Years ago Vitus and Alan made aluminum framed bikes that used the same tubing diameters as the steel framed bikes of the time. They were comparatively light and quite flexy. Along came Gary Klein who decided to make an aluminum frame bike with the same amount of material but larger diameter, thin wall tubing. The flexiness went away.

Materials do have properties but it's the total design that determines whether a bike frame will be stiff or flexy.