Perhaps the distinction has to be made between flat (where all of the points on the board face occupy the same geometric plane) and smooth (where the surface of a rough sawn board has been removed, but not necessarily such that all of the points of that board face occupy the same geometric plane).
As an example, if you set your jointer to remove 1/16" and power feed a board that has a 1/4" bow, the feeder will press the board down at the point of cutter contact and remove increments of 1/16" along the entire length of the board, but you are not removing the bow, you are removing 1/16" of material. You might just as well run a rough board through a planer.
Hand feeding a jointer allows the irregularities of the board to "float", in this case removing 1/16" from both ends of the board but not the middle, and repeated passes will take more material from both ends until the board face is flat and smooth, instead of just smooth. (Yes, crown down is the proper way to remove a bow, but this is for illustrative purposes)
A stack of properly faced and planed boards will be solid, with no gaps between the boards and no rocking of the stack. The same can not always be said for a stack of boards prepared in another manner. Again, it depends on your intended use. If you are making doors, windows, or panel assemblies that interface with doors and windows, you will want flat stock. If you just need smooth boards, any method of smoothing them will do.
You will note in the first video that Mark posted that the operator makes a point of showing the edge of the board with a bow prior to power jointing, but does not show it after jointing, perhaps with good reason, such as the very likely possibility that the bow is still there.
FWIW. YMMV.
Tone