As far as I understand the physics of how all this stuff works:
The stiffness of your frame has a lot more to do with the size and shape of the tube than the wall thickness. And heat treatment and steel type have pretty much nothing to do with stiffness, they are just about dent resistance. The real "advantage" of using the fancier steels (True Temper S3, Columbus Life or XCR, Reynolds 953, etc...) is that they are much harder to dent. This allows you to use a thinner tube wall without it crumpling like a soda can under usage. Hence you can make the tubes larger in diameter, giving you a stiffer frame.
I had a chance to chat with an engineer from Boeing about this stuff a little ways back. He told me that tube shape and diameter is so important that it pretty much trumps even what material the tube is made of. Crazy. That means that what your frame is made of actually means very little. Carbon fiber, aluminum, bamboo, titanium, steel. Doesn't matter as much as one might think. It also plays into the idea that carbon and aluminum frames are "stiff" is not because of the material itself. But it is because of the particular properties of those materials, namely a very low weight to volume. This enables you to use a larger diameter tube and not have it weigh a ton, giving you a stiffer frame.
The bigger question to me, and the design problem I work with as a framebuilder, is what are the appropriate tube diameters to use for any particular customer. How to give you the best riding bike for the purpose you want to use it for. Having the stiffest bike frame possible is not always the best option. Too stiff and your ride quality gets really harsh. Some folks think that flexible frames ride better and return power back to the rider as it springs back. Popular theory states that the stiffer the frame the better. I kind of fall somewhere in between. I want each customer to be happy with the bike they get. If you want a frame that is as stiff as can be, so be it. If you want a frame that "planes", I can do that. Every custom bike that I make is tailored to the person it is made for. And (I hope) will ride in the way they want it to.