Yes, this is really how it works, and Bernoulli should be left in the dustbin, since in comparison it's a smaller effect, with more impact for carburetors than aircraft wings.
One small anecdote: the first time I flew a 1-26, I got it a bit slow, and a loud noise and vibration started to come from the flat tail at the rear. Of course, this was me approaching the top of that curve, where lift is lost and the surface stalls. I called ground, and they told me to fly a bit faster, and of course the noise abated.
Anyone who's interested in flight should go fly a sailplane. It really is one of the most awesome experiences a human can have.