Indeed there is no "pull" from sucking, pressure can only push.
Most of the lift is due to the top surface geometry, hence 4/5 coming form the top of the wing. Take away that geometry and it just doesn't work the same way.
The spinning cylinder directs as much air up as it does down - we can't choose to ignore the upwash and only look at the downwash, so yes the air is re-directed, but as much up as down. Resolving the entire flow, as much momentum goes up and goes down, so the skipping stone theory doesn't add up. There are further links on the NASA page I linked to above.
There is no need to "attach" low pressure to the wing - the wing is pushed in to the air by the high pressure below, but its the top surface that creates the low pressure that makes the pressure below the wing the higher of the two.
Certainly the skipping stone theory is incorrect, although along with the equal time fallacy, there may be truth mixed in with the error.