You've got it backwards about the role of oxygen--it is being used to inhibit polymerization in this case. They are allowing oxygen to dissolve into a thin layer at the bottom of the vat so that the build doesn't stick to the membrane, and they can have a continuous draw.
The true build layer is actually within the liquid, near the bottom, but not on it.
You're totally right. Oxygen inhibits the polymerization process. Interestingly, oxygen inhibition is also what allows things to be printed in layers (or, in this case continuously) as it allows the newly cured material to bond to the partially-cured inhibited material below it.
The true build layer is actually within the liquid, near the bottom, but not on it.