The simplest way that I can explain why you should primarily "believe" Newton's explanation is to look at a helicopter or at an aircraft propeller. Simply put, helicopters fly because they accelerate a mass of air downward. Likewise, propellers accelerate a mass of air backwards to produce thrust. Airplane wings accelerate air downward in exactly the same way. Airplane wings are relatively large and therefore less acceleration is taking place on a larger mass of air than with a propeller.
I was recently reading Skip Smith's "Illustrated Guide to Aerodynamics" and was very disappointed to only see three short paragraphs that dealt with lift due to momentum change.