I ain't pulling your leg. I was surprised, indeed, a very long time ago to find that the mechanical property 'modulus of elasticity' was the same for stainless and carbon steels.
I could quote you the formulas if you like, but basically the stiffness of any uniform member is related to its length, cross sectional area, and modulus of elasticity. Both steels have a modulus of around 29 or 30 million pounds per square inch. This means that barrels with the same dimensions will be equally stiff whether they are made of carbon or stainless steels.
Stiffness isn't the same as ultimate strength, nor is it the same as machinibility, hardness, or toughness. This stuff gets complicated.
I'm a mechanical engineer, and not a metalurgist. I used to be employed as a mechanical analyst in the aerospace industry. We used 29 or 30 million psi for both steels.