Your explanation is, in fact, the correct description of the process. Gravity causes the liquid in the long end of the tube to fall, which creates a pressure differential along the length of the tube, which atmospheric pressure on the to-be-emptied liquid attempts to "correct".
Professor Hughe' definition can be found here and he claims that the siphon action has been demonstrated in a vacuum (footnote 3.)
His explaination relies solely on gravity and the molecular attraction of individual water molecules to form a "chain" that is pulled up and over the hump, in the same way that a chain and pulley work.
It would be simple to test which theory (atmospheric pressure or gravity alone) is correct by building two sealed boxes connected by a flexible hose. Each box would be halfway filled with liquid, then the atmospheric pressure drawn out of the empty space above the liquid in both containers. Once the hose is filled with water, lowering one container below the other container should begin liquid transfer. Switching the positions of the two boxes should reverse flow. If water flows, then gravity is the root cause of the siphon action.
Alternately, one Atmosphere is roughly equal to 34 feet of water. Try to create a siphon that can lift water higher than 34 feet before it makes it's turn downwards. If the siphon action stops when the lifted column of water exceeds 34 feet, then atmospheric pressure is the root cause of the siphon action.
Doesn't need to be atmospheric pressure, the weight, and thus pressure of the liquid in the tank would be enough.
However, this Ozscience wannabe boffin is operating in the antipodal region and due to the Coriolis Effect, his mind has been weakened by bath water swirling the wrong way since childhood,crikey, and stone the crows.
Also, being raised on wichitee grubs and chased by salties has been shown to stunt the growth of cerebral cell structures. Treat with Foster's frosty amber fluid (comes in tubes) and bed rest.