This is correct.
> A hollow steel tube the same weight and diameter as a solid aluminum
> shaft is probably stiffer.
Yes, it is very slightly stiffer (by a few percent, I think). The key to any structural design (for optimizing weight) is to get the section modulus up. Basically, getting the material concentrated at the outer surfaces of a member. What the tradeoff of steel vs aluminum usually comes down to is which one is easier to work. This is usually aluminum for the typical hobbiest, but not always so (armed with a cheap welder, you can fabricate a very nice mount). Aluminum looks good unpainted, too (or anodized...). One of the nice attributes of steel vs aluminum for some parts is the lower coefficient of thermal expansion.
Bob