A contradiction from two reliable sources on the principle of how siphons work

There is no contradiction between the two sources.

Siphons are permitted by physics because fluid flow through the siphon lowers the fluid's overall energy, since the output end of the siphon is lower. The main requirement for them to work is that the fluid moves together through the siphon. That, in turn, doesn't technically require atmospheric pressure (and doesn't even require that you have a fluid, e.g. see the chain fountain).

Walter Lewin is pointing out that in practice, siphons are hard to get working above ten meters. The reason is that at that height, the fluid would be flowing with negative pressure, i.e. it could spontaneously turn into vapor, which would ruin the siphoning effect. In other words, atmospheric pressure is technically playing a role -- but it's simply the same role it has in everyday life, i.e. preventing all water from spontaneously boiling.

That is not in contradiction with the video you linked, which uses a specially engineered liquid that is stable against this.

A pressure that is less than the vapour pressure of the liquid can make liquid form vapour bubbles.

Then again, a pure liquid that has no already-formed bubbles needs some extra effort in order to create bubbles. At low enough temperature, the surface tension makes possible for liquids to withstand some negative pressure without forming vapour bubles.

The effect can be engineered to exceed the atmospheric pressure by using thin enough (capilar) tubes. (That's how tall trees get water from their roots all the way to their leaves way above 10 meters. There are 100+ meter trees.)