The way they are packaged is important. Some salad greens are packed in a nitrogen atmosphere, which means the air inside the bag has had all the oxygen removed and replaced with nitrogen instead (normal air is 78% nitrogen so increasing this up to 100% is of no health concern). But it means oxygen-breathing bacteria on the leaves will find it difficult to grow inside the sealed bag (at least until the oxygen gets back in, one way or another), prolonging the life of the fresh greens.
If you empty them out of the bag then you are providing the bacteria with a literal breath of fresh air, helping to kick start them on their journey of turning your fresh greens into compost.
I'm also not sure that cut leaves do much in the way of oxygen production. For a start, once removed from the plant they no longer receive fresh water and nutrients from the sap. Oxygen is also only produced during photosynthesis, which requires light. So if the light is off in your fridge when the door is shut, they won't be able to produce any oxygen anyway. (In fact most plants stop taking in carbon dioxide in the dark and consume a small amount of oxygen instead.)