no need to go to the moon
You don't need to go to the moon to test whether atmospheric pressure is responsible for siphoning. Just put a hole at the highest part of the hose and see if the siphon keeps working. It is atmospheric pressure (and a little surface tension, I guess) that stops the fluid in each side of the hose from separating and flowing back into its respective container.
Bootnote: The fact that the pressure is (roughly) balanced at each end of the hose is not the whole point. The important part is that the pressure is not enough to counter gravity on the long side, so the fluid flows down, whereas it is more than enough to counter the gravity on the short side (which weighs less) so the fluid flows up.