Just the opposite. 1.2cm vs 1cm might be a world of difference. And if weight is a concern, you might be stuck with a 1cm tube, which might be less stiff than the 1.2 cm tube even if it's made out of a stiffer material.

The idea is that design is material dependent. You can't assume you can just swap out parts for lighter/stronger/stiffer parts and still have everything work.