Yawn...............
Any reputable test book will tell you that there are several theories that have been developed to predict the performance of an aerofoil. The Equation of Continuity (that's the one that uses Bernoulli's Theorem) is but one (the most used, granted). There are also Momentum Theory (I personally prefer this one), Circulation Theory and Dimensinal Analysis that I am aware of.
The Equation of Continuity just happens to be the easiest to understand and is therefore the most widely used.