There is a big difference between the mathematical modelling of the flow and the actual flow. The wing can be modelled as a sheet of little vortices - but we know in reality a wing doesn't work like this.
How can pressure distribution and downwash be the same thing?
If it were just about "throwing air downward", then why don't curved plates that generate downwash but a poor pressure distribution generate so little lift?
Have a look at
FoilSim II 1.5a beta
By being a bit creative with your entires to the boxes, you can generate lift with more upwash than downwash. OK, its a sim and not a real windtunnel, but I doubt it is so inaccurate that it is not representative.
For instance, try angle -20 deg, camber 24.5, thick/cord 16.725. You will have a lift of 797 llbs, so its not very efficient as a lift producer, but the air is visibly going up more than it is going down, so there is no net downwash.
Similarly, set the angle 9.56 deg, camber -8.1, thick/chord 12.775. The flow from the back of the wing is slightly upward (see the jink in the pixels on the line) and it is generating a small amount of lift (again, albeit inefficiently).