Since he had to go to some length describing the troubles he had because the low pressure formed bubbles due to cavitation, etc. (remember he could not perform this at zero atmospheric pressure because the water would boil), why use water?
Why not use a liquid that will not boil in a vacuum, like (I think) mercury? That would very easily prove that atmospheric pressure is not required to make a siphon work (because there's no atmosphere!).
Take a flexible tube and dunk it in a bucket filled with mercury letting it fill up. Now, sealing the ends, keep one end in the bucket while lowering the other end to another bucket positioned substantially below the first. Pump all the air out of the chamber and unseal the ends. If the siphon works, it is definitely solely due to gravity (remember there's no air!).
Actually, not knowing what the intermolecular bonds are like between mercury molecules, will the siphon still work? If mercury molecules have little or no attraction between them (unlike water which has very strong intermolecular bonds as seen with its high surface tension and high boiling point), perhaps it would behave like discrete particles and there would not be any siphon effect. For example, imagine the bucket and tube to be filled with sand. Would there be a siphon effect? I don't think so because the grains of sand wouldn't "pull" on each other so the sand in the tube would just run out in both directions from the high point in the tube.
Another way to think of the intermolecular bonds is to think of a coiled chain which is held aloft. If a part of it is pulled over a pulley and a substantial length is allowed to dangle down the other side, the rest will be pulled up to the pulley and then down. Of course if all the links in the chain are broken (no intermolecular bonds) then the chain will simply fall away from the pulley on both sides.