Sweet Shooter, if you remove several long strips of metal from the outside of a rifle barrel, you've removed some of the material that resists bending. It's gonna be less stiff 'cause there's less metal resisting bending.
Winchester's fluted barrels have the same outside profile and dimensions of their standard ones. I talked to one of their engineers years ago when I first saw their claim about it. He agreed with me and was aghast that their web site would make such a claim; then he laughed when he actually saw it.
Check this link out; especially the part about folded flat stuff: