It's not atmospheric pressure, it's internally induced pressure due to buoyancy differences, which are normally created due to gravity and a connection that is rigid enough to withstand the internally induced pressure. If you have a closed system of two non-rigid containers connected by a rigid body, then the fluid will try to flow in the direction of its buoyancy. Helium balloons connected internally by a straw (even a curvy one) would try to fill the higher balloon, right?
So yeah, he's right that in the absence of gravity, a normal siphon will not work. But, if you took that siphon system on the ISS and put one end outside in space, and one inside, you'll have a siphon-like effect due to air pressure. Likewise, if you take two balloons of water with a rigid connector and submerge one in a pool of Hg, then that "siphon" will work against gravity. :D