I believe the deflection is the high-level explanation. Things like the Bernoulli effect and the air on the top of the airfoil travelling faster (it does -- far faster than the equal transit time theory implies actually), are the "instantiation" or outcomes of the air deflection. This is my understanding. Hence airplanes can fly upside down because even if the airfoil is upside down, it's still deflecting the air, just perhaps less efficiently (I think it's true that planes flying upside down need a more extreme angle of attack to maintain lift, so this makes sense)