In the short term, oxygen can be termed a 'friend'. But if you befriend him long enough, all of his vices will come out and your oil will lose its original character. True, it might smell aged and look thicker than before, however its shelf life has been deeply compromised.
What the lady told you about the gas sounds paradoxical. The gas is supposed to shield an oil / perfume from oxygen by creating a barrier, yet they don't use it on sandalwood because oxygen would affect the oil? Sounds like there wouldn't be much of a barrier after all.
If an oil is left to mature without being exposed to oxygen, its aging will occur much slower than if force-oxidized. There is a fine line between aging and oxidation, which is what happens when you expose an essential oil to oxygen. The effects might smell and look similar to the unsuspecting, but there are profound chemical differences between them.
Apply the same thought process to food (like two jars of brine-fermented vegetables, for example) and you've got the difference between major health benefits in the tightly-sealed, air-protected jar, and contamination and toxic moulds in the jar with exposure to air.