You got it wrong, Keith.
Putting it simply, if it weren't for a depression ("vacuum") in the manifold there wouldn't be any air movement over the jet. The same depression draws the air valve upward.
Nope, not the same depression. The chamber over the piston is open to the venturi, so it "sees" roughly the same depression as the venturi, which is more or less constant. (That's the constant depression in "constant depression carburetor".) The manifold vacuum is on the other side of the throttle plate.
If you put manifold vacuum on top of the piston, it would simply slam to the top as soon as the engine started. Normal idle is around 18" Hg, roughly 9 psi below ambient. The piston in an H6 is about 3" in diameter, so has an area of about 7 sq in. 9 psi times 7 sq in would be 63 pounds of force pushing the piston up.
Think of it like washing your hands. The pressure inside the water pipes is what pushes the water out, sure, but it is much higher than the pressure at your hands.