1) The claims are not supported by or at least reference any scientific proof.
2) My own humble experience of thermal soaring partially contradicts with common beliefs.

I have many times witnessed long living dust devils. They are good examples of a non stationary point of detachment of hot air from the land surface. They actively move instead of being fixed to some special point like top of the heel. Dust devils (not tornado) also can appear above water surface, so it looks like unstable layer of overheated air can magically ignore heat contrast between land and water.

Large thermals also behave similarly...Well, at least some of them.

In springs, when people burn old leaves, the smokes of fires converge and literally show you the point where thermal is. Being 1500 meters above the ground allows you to notice that the lowest part of the thermal moves quite noticeably even without background wind and do not stop where forest begins.

The only practically useful book about thermals I have read so far is Scorer R. S. Environmental aerodynamics, Ellis Horwood Limitid Publisher Chichester. — N. Y., 1978. Though Scorer writes much about thermals structure (jets, plumes, thermals), he says almost nothing about how exactly unstable air is perturbed to give a birth to a thermal.

The part that has lifting power most is column because it picks up speed and momentum while it spins and whirls like the water draining into a sinkhole. The rising column can be pushed and swivel around by wind or topology of area surrounding it. The source of energy is dark surface or topology or local climate that can create layered temperature gradient from hot near ground to cold at altitude. Of course as we pilots of small planes know there are many other factors involved specially in mountains. Fire fighters are keenly aware of the tunneling effect and unpredictability of thermal near the canyons.