These are all assumptions, but that doesn't mean I can't argue about them until the choppers come home!
I picture the actual, rotating wheel for this to be roughly what you'd get if you cut the spokes off of a regular wheel, and machined a (cross sectionally) flat surface onto the inner face. Now take a hollow axle, and put it on your axle stretching machine, and crank it up so the outer face of the axle is big enough to come within a few mm of the inner diameter of the wheel's inner face. Leave enough room for a bearing, put the bearing between the 'axle' and the wheel, and then put it all together.
Unless I'm hugely mistaken about how these wheels are built (a distinct possibility, I'll be the first to admit), the result will be a large, non-rotating 'axle', and a wheel/tire assembly with much less mass than a conventional setup. Maybe the "double-rim" you refer to is what I'm calling the 'axle' and wheel. If so, I'd still think only one of the two pieces that make up the double rim would rotate.
As for stiffness, I think a wheel gets a lot more of it's stiffness from the lip against which the tire bead seals than from anything else. And the wheel is in contact with this big, strong 'axle'/double-rim, and that will also add stiffness.
Any Mechanical Engineers out there care to chime in? This is just a phyzzicist makin' it up as he goes along here...
I sure hope this thing handles better than a wet cucumber approaching an icy bridge!