We need to introduce some basic physics here...
The "angle of thrust" -- the angle between the ground and the line running from the tire contact point up to the center of gravity of bike+rider -- is determined solely by the speed and the radius of the turn. The downward pressure at the tire will, on a reasonably bump-free road, be precisely the weight of bike+rider (divided between the two tires, of course), while the outward pressure -- the tendency to skid out, as it were -- will be determined by the laws of centrifugal force. If you know those two forces you can use the squaw on the hippopotamus to compute the "thrust" along the center-of-gravity line, and you can use trig to figure out what the angle to the horizontal is.
So whether the cyclist leans in or out makes zero difference in the thrust (and tendency to want to skid out) -- it's purely determined by speed and turn radius.
With an essentially cylindrical tire cross-section, the amount of friction (to resist skidding out) will be primarily determined by the coefficient of friction of the tire material and the downward weight on the tire. Since a road tire has essentially the same coefficient of friction over its entire usable surface, the "lean" of the tire has little effect on traction.
There will be some degree of effect on traction based on how close to the rim one is, and how the tire is deforming -- it could be reasonably argued that as a tire is leaned and deforms sideways more it will "squirm" more, resulting in some loss of traction. But this effect would be slight on high-pressure road tires.
The two major effects to consider here are more mechanical. One is the way the geometry of the bike+rider changes as the bike traverses minor bumps, and the other is the way that steering behaves.
With regard to the bumps, consider two cases: 1) The bike is essentially vertical, with the rider leaning into the turn to achieve the right angle of thrust. 2) The rider attempts to stay vertical while leaning the bike (and necessarily the lower portion of his body) into the turn.
In the first case, when a bump is encountered, the bike will be pushed upward, with the "pivot" of the rider's body bending to absorb the shock. There will be little change in the overall "geometry" of the "system" (though there may be some change in the geometry of the rider's back, requiring chiropractic services to correct). In the second case, the rider will remain relatively motionless while the angle of bike to road changes dramatically. I think it's clear that, other factors being equal, the second case will result in a less stable behavior.
With regard to steering behavior, consider how much change in direction occurs for a minor change in steering angle. With the bike essentially vertical the radius of the turn is determined almost completely by the steering angle. It takes a relatively major change in steering angle to effect a change in turn radius.
On the other hand, with the bike leaning the radius of the turn is affected by the curve of the bike tire -- as the steering angle increases the point at which the tire touches the road moves forward along the wheel diameter, so that a minor change in steering angle produces a much more pronounced change in turn radius. But an interesting side-effect of this is that as the bike leans more it tends to turn more sharply, and turning more sharply increases outward thrust, tending to right the bike. This results in a relatively stable steering configuration.
The net-net of this to me is that on a relatively smooth road you'd want to lean the bike "naturally", to achieve optimal stability (not only for speed/safety but also to reduce rider fatigue). However, on a less ideal surface one might not want to lean so far. (Of course, a relatively prudent rider would not ride as fast on poor surfaces anyway, so naturally there would be less leaning.)
But I suspect that a lot of how people ride (including the rider in that video) has to do more with body mechanics than bicycle mechanics. On a long downhill the rider is taking the opportunity to rest, but also having to be ultra-alert to avoid wiping out. Certain body configurations will permit more relaxation/recovery of the major muscles while at the same time optimizing control and the ability to comfortably "ride out" the shocks that one experiences at high speeds even on a "smooth" road.