Now that we've all slagged the theory off I'd like to put a few points in its defence (without implying I actually support it) (though it would need amending) -
The lack of evidence of such balls isn't significant - a few dozen, used repeatedly, is all you'd need so the fact none have been found isn't necessarily significant.
I don't think their idea of two precise grooves for them to run in is necessary. Wide grooves, say 9 inches wide into which balls were thrown randomly would support a moving "stone-barge" adequately.
The above arrangement would mean all the balls wouldn't necessarily have to be of identical size as there would be a tendency for them to migrate laterally and take up a supporting position wherever the underside of the barge was subject to variations.