XP
I agree you are right with your two main points.
However, there is a theory which (I believe) goes as follows (I just know I'm going to regret this!):
Although the air approaches the wing horizontally, the air off the back of the wing departs the wing with a downward vector (downwash).
As a result, the relative total airflow past the wing is not horizontal, but descending.
As the lift is perpendicular to the relative air flow, the overall lift is not purely vertical, but has a rearward component - this rearward component is drag.
Ground effect removes the downward component of the relative airflow (the air leaves the wing horizontally) which means the lift is all vertical - i.e. less drag...
...so I'm told.