This is not an official vet-recommended treatment for skunk spray for a couple of reasons. The active ingredients in OxiClean (and similar products, which would also work) are sodium carbonate (washing soda) and sodium percarbonate. They react to form peroxide, which is an effective bleach and disinfectant, plus is reactive enough to tackle most messes. It's also reactive enough to cause damage to certain tissues. If you read the MSDS for sodium percarbonate, for example, you will find the chemical is harmful if swallowed and may cause severe eye injury. If you spritz OxiClean in water on yourself or your pet to remove skunkiness, you need to be absolutely certain to avoid getting any in the eyes. Plus, you need to take extra care to rinse all of the OxiClean off. You might not lick your hands after washing them, but chances are your cat or dog will.
How does it work? OxiClean should work as an odor remover pretty much the same way as it works as a stain remover. The hydrogen peroxide that is released reacts with stain molecules and changes their structure. This makes them absorb light differently, rendering colored stains colorless. Note that this does mean the stains are actually gone; you just can't see them. Stink molecules are like stains. If you change their shape, the chemoreceptors in your nose may be unable to detect them.
So... if you have an encounter with the business end of a skunk, try reaching for the Oxiclean instead of the V-8. Avoid the eyes and rinse, rinse, rinse.