If you look at the speed and thus energy above the immediate boundary layer it will be close to the free stream air speed and thus you still have accelerated air speed and therefore reduced static pressure.
True. But saying Bernoulli is responsible for this is exactly what this paper was highlighting as a 'myth'.
But the general effect (Air accelerated creating low pressure and thus lift) will still be there.
Not true. Lift is directly related to the downwash of air. The article also explained that the acceleration of air DOES NOT create the low pressure - the low pressure causes the acceleration of the air.
If you have air flowing around an airfoil that is producing lift you will have a relative high pressure on the bottom and a relative low pressure on top. If you are saying that since there is a low pressure on top and high flows to low, the wing will get pushed/sucked up - that's not really true. Air has to get deflected to create 'lift'. If air is not deflected by the airfoil, there is no net force and therefore, no lift. That's also why spaceships need retro rockets in space to maneuver because there is no surrounding atmosphere where a change in shape of the spaceship would produce a net force - they need to apply a net force by expelling mass at a high velocity (rocket). Putting those two together, if there is a low pressure, the air will flow in the direction of the low pressure - which is upwards. If the air flows upwards, according to Newton's 3rd law, there will be an equal and opposite
down force on the wing. That's the opposite to lift!