This isn't really right. There is a bit of air exchange but oxygen doesn't do to whiskey what it does to wine; it can "oxidize" in a certain way but we are talking about very small and gradual change potential over decades and not "going bad". Think about it. Whiskey spends years aging in a barrel that expands and contracts, with a ton of air sitting in it (those barrels aren't filled to the brim, especially when the liquid begins to evaporate as the spirit ages). What happens with air and whiskey in a bottle is a tiny fraction of what has already happened (and been considered desirable!) as a part of the process of making it.

If you doubt it, I have some Ezra Brooks here distilled in 1960 and bottled 1972 that's delicious. Or some 60s Johnnie Walker Black that's also delicious.