I won't disagree with what you said, Deemar, but having the precise definitions about what the author in the NASA article (I don't have it) says could clarify things for us.
I have heard the theories broken down to Bernoulli being the portion of lift due to the difference in pressure and the remainder being due to the deflection of the free stream. You can describe the latter with coanda effect if you wish.
The point is, most of the descriptions of Bernoulli's theory don't discuss what happens to the air aft of the trailing edge, which as Nick points out is the lift that we can comprehend easily, and it is the majority of the contribution of the total lift according to the spectral NASA report on "incorrect theories".
If we only look at the deflection of the airflow, or more precisely the change in momentum of that airflow, then we miss the small contribution to lift due to the pressure differences.
So without seeing the NASA report, I can understand why someone may look at the theories in such a way as one being a small contribution and another being the most significant.
In the end, it doesn't matter too much to the average pilot. I disagree that line pilots don't need to know the lift equation. Understanding what your aircraft is going to do when conditions change is important, and I believe the lift equation is a good teaching tool to help us develop some anticipation. How you derive it doesn't matter too much because the formula that we use works well enough for the majority.
Matthew.