It doesn't make any sense to me, the idea that the foam disappearing would indicate that there is nothing to this method. I would expect the foam to disappear - what else could it do? The role of the foam is to have greater surface area for oxygen to get absorbed. Once it is absorbed into the wort the job is done - the oxygen has saturated the wort. But maybe I'm missing what is being said above.
But is the oxygen in the bubbles really absorbed back into the wort, or is it just encapsulated in the foamy bubbles? Once the bubbles bursts, the O2 is just released back into the air, not into the wort. Just like using a stone, if the O2 is bubbling to the surface it is escaping, not absorbing. It would seem that any O2 absorption occurs during the shaking, not as a result of the collapsing foam.