rightish, but hoist by his own petard
Hmm. There are subtleties here that deserve more care than the superficial treatment doled out by Weaver.
Obviously you need atmospheric pressure for the sucking bit at the start. But that's a red herring. The siphon could also be started without an atmosphere, by a piston or propeller in the pipe.
However I think that a siphon would not work in a vacuum. Without outside pressure on the water, voids (ie. bubbles of void, nothing) could freely open up within the water at any point in the pipe. The water in the downward leg could happily flow downwards, leaving the upward water where it is. Between them would be a void. The "downward" water could exert no force on the "upward" water to pull it over the lip.
With an atmosphere, such voids cannot form because atmospheric pressure tends to close them up. Bubbles of air can form, of course, and can break the siphon if you are careless enough to let the required amount of air in. The siphon depends on the water remaining in one coherent flowing body.
It might be possible to form a very weak/slow siphon in a vacuum. The self coherence of the water might be enough to stop voids forming and hold the water together if the tube were very narrow. But I think that would be capillary action, not a siphon.
Which proves how idiotic it is staying up this late on a Tuesday morning to make my overblown points in the folorn hope that somebody somewhere will be interested. Still, I now feel confident that my toilet will not work on the moon, which is bound to save embarrassment sooner or later.