Atherosclerosis starts with transmural (transwall) pressure-driven advective transport of blood-borne low-density lipoprotein (LDL) cholesterol across rare endothelial cell (EC) monolayer leaks into the arterial subendothelial intima (SI) wall layer where they can spread, bind to extracellular matrix and seed lesions. The local SI LDL concentration, which governs LDL's binding kinetics, depends on the overall diluting transmural liquid flow. Transmural pressures typically compress the SI at physiological pressures, which keeps this flow low. Nguyen et al. (2015) showed that aortic ECs express the water channel protein aquaporin-1 (AQP1) and the transEC (δP) portion of the transmural (ΔP) pressure difference drives, in parallel, water across AQP1s and plasma across interEC junctions. Since the lumen is isotonic, selective AQP1-mediated water flow should quickly render the ECs' lumen side hypertonic and the SI hypotonic; resulting transEC oncotic pressure differences, δπ, should oppose δP and quickly halt transEC flow. Yet Nguyen et al.'s (2015) transAQP1 flows persist for hours. To resolve this paradox, we extend our fluid filtration theory Joshi et al. (2015) to include mass transfer for oncotically active solutes like albumin. This addition nonlinearly couples mass transfer, fluid flow and wall mechanics. We simultaneously solve these problems at steady state. Surprisingly it finds that media layer filtration causes steady SI to exceed EC glycocalyx albumin concentration. Thus δπ reinforces rather than opposes δP, i.e., it sucks water from, rather than pushing water into the lumen from the SI. Endothelial AQP1s raise the overall driving force for flow across the EC above δP, most significantly at pressures too low to compress the SI, and they increase the ΔP needed for SI compression. This suggests the intriguing possibility that increasing EC AQP1 expression can raise this requisite compression pressure to physiological values. That is, increasing EC AQP1 may decompress the SI at physiological pressures, which would significantly increase SI thickness, flow and subsequently SI LDL dilution. This could retard LDL binding and delay preatherosclerotic lesion onset. The model also predicts that glycocalyx-degrading enzymes decrease overall transEC driving forces and thus lower, not raise, transmural water flux.