Now you see it, now you don't. The amount of oxygen you can supply to the legs is dependent on lung volume and breathing rate and you can't do anything more if those two don't add up to the climbing rate. They are intimately linked and the efficiency of these is dependent on conditioning the muscles to receive that supply.
So we understand that the endurance of our legs depends on the ability (of our bodies), to distribute oxygen through our bodies, to the parts that really need them.