I would venture that the biggest factor in hands-off riding is rider input. I recall touring on my '75 Gran Crit with panniers on a rear rack and being able to reach into my rear jersey pocket, grab an orange, peel it and eat it without once having to grab the bars. Just last summer riding my Rex bike on the Northwoods Tour I managed to snap several hundred pictures from the saddle, no prob. I think the French have a word for it: suplesse...(SP?). Riding the fixie is a good way to start.
Nor in Iowa