I think that when people say that a siphon works by gravity, they mean that gravity is the driving force that makes the water flow through the tube. You have shown that you need ambient pressure to make a siphon work, but that is similar as saying that you need a tube to make a siphon work. Saying that a siphon works by gravity and ambient pressure is equivalent to saying that a gas engine works by burning gas and sparks.
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I think that when people say that a siphon works by gravity, they mean that gravity is the driving force that makes the water flow through the tube. You have shown that you need ambient pressure to make a siphon work, but that is similar as saying that you need a tube to make a siphon work. Saying that a siphon works by gravity and ambient pressure is equivalent to saying that a gas engine works by burning gas and sparks.
The plants that you burn in the machine pulled the carbon out of the air for you while they growed. Therefore the process is carbon-negative.