C. botulinum is an obligate anaerobe, requiring an environment that lacks oxygen. However, C. botulinum tolerates traces of oxygen due to the enzyme superoxide dismutase, which is an important antioxidant defense in nearly all cells exposed to oxygen. C. botulinum is able to produce the neurotoxin only during sporulation, which can happen only in an anaerobic environment.
I've never once seen it said that the toxin is destroyed by exposure to oxygen, and can't find such a claim on Wikipedia. If getting rid of the toxin was as easy as stirring the crap out of food for a few hours, the universally prevailing advice wouldn't be to avoid food in swelled cans like your life depends on it (which it does).