This is one topic that annoys me a lot as an engineer.
First thing I want to say to pilots is "stop trying to understand how a plane generates lift at an engineering level". What you have been taught is bullshit, and its not necessary.
Second, to the pilots who say there is no proof, well look at what you do for a hobby/living. I would say the fact that a plane is in the air, and can be put in the air repeatably is scientific proof that its possible. If you disagree with that proof, then please show me that planes do not fly.
When I first started flying, I was told to read the book stick and rudder, and the author nails is perfectly. The reason a wing produces lift is because its deflecting the wind downward. Stick your hand out a car window at speed and you have the perfect example. That and a little Bernoulli WRT to stall characteristics of wings is all that is needed so you can understand how a stall horn works. I only watched a little bit of that video (its also laced with bullshit) but I think the author is pushing that same concept. I hate plagiarism, and the credit needs to go to the author of stick and rudder (just looked it up on Amazon, Author is Wolfgang Langewiesche)
As for the engineering side, no one use Bernoulli or Newton exclusively, they use many different theories/models including many which most pilots would never even be privy to in ground school. Whilst I dont do aerodynamics (although I did touch on it at uni, and spent a lot of study time with an aeronautical engineer), I have spend countless hours with other engineers making instrumentation to measure various aspects of fluid dynamics. Engineers know how planes fly, thats how engineers design planes that fly.
I read here a lot, but I remain silent because as a low hour (just recent) PPL I probably dont get the credit that a 20,000 hour CPL or ATPL would. But I do understand the basic physics of flight, and I often see those 20k hour pilots regurgutiating that same bullshit they were taught and its plain wrong. When I did my PPL theory, I wanted so bad to point out incorrect information that is taught and tested, but I cant, because I had to be tested on the same rubbish.