I'm with Don't Hang Up on this one.
Take it to an extreme, you have a vessel of water on one side of a wall that is 36' tall. On the other side you have a receiving vessel that is 10' lower than the first vessel.
This will not siphon. Once you've managed to suck* the water to crest the wall the water in the tube will drain to both sides again.
Lower the wall to 20', it will siphon, as atmospheric pressure is pushing the water up over the wall allowing gravity to pull the fluid through the rest of its journey.
Dependent on the fluid and the pressure depends on how high one can make the 'wall'
Both are required in my opinion.
(Good point that gravity is why there is atmospheric pressure in the first place though...which does make it purely based on gravity breaking it down to first principles)
*for sake of brevity, suck was used but if you wish...once you've managed to reduce the pressure on one side of the tube sufficiently to have atmospheric pressure on the other side force the water through the tube...(LM, I don't recall that level of pedantry when you taught me for the ATPL's
)