This isn’t my medical opinion, but I have seen that method in books and on culinary shows, using raw peppers, so I imagine its safety is proven.
Clostridium species produce very tough spores, which are often very resistant to heat, dehydration (e.g. alcohol) and other common methods of sterilization can be found in ordinary soil, but contamination poisoning is limited to a few situations because C. botulinus is an anerobe: it hates oxygen
Further, it is very common for liquors and wines to be aged for many years or decades, but I’ve never heard of C. botulinus growing in them. Vodka is essentially just water and alcohol, and it seems biochemically plausible that an anerobe like C. botulinus won’t use use alcohol as a fuel – but I wouldn’t bet that some anerobe couldn’t metabolize alcohol. Mostly, the high concentration of alcohol probably keeps the spores too dry to “sprout”. Air-Drying, and curing with salt or sugar to decrease moisture are all age-old methods of preserving food.
Oxygen is so reactive that it’s generally a toxin; it was a poisonous waste product early in the history of life. Then ancient microbes contaminated the environment with so much of it that many species evolved to make use of it. In fact, if you wanted to prove the existence of life on Earth from deep space, our highly reactive oxygen-rich atmosphere would probably be persuasive evidence. Kill all life on Earth, and all our free oxygen would eventually combine with other chemicals.
Even today, possible the majority of microbe species prefer to avoid oxygen. Its radicals, like peroxides, are used as a weapon against microbes by our own immune cells. Aerobes (oxygen-using) do have one advantage: they tend to have faster metabolisms because oxygen participates in energetic reactions with most common organic substrates. Foods spoil faster when aerobes get to them, and being Aerobes ourselves, we encounter more of them in the places we like to live.
Classic botulism comes from canned foods where the oxygen has been sealed out to prevent the growth of fast growing food-spoiling aerobic bacteria. It’s not an infection, but a poisoning with a potent bacterial toxin that accumulates as the C. botulinus slowly grows. Infant botulism is an entirely different beast: C. botulinus spores from, say, honey, which wouldn’t hurt most children or adults, can find a home in the relatively oxygen- and competitor- free infant gut, and grow there, eventually poisoning the baby from inside. (That’s why you shouldn’t give honey to babies, per the American Pediatric Assn. Even pasteurization and heat treatments might not kill all Clostridium spores; they’re extra tough.)
In both classic and infant botulism, the Clostridia grow in a relatively oxygen-free environment. If we want to grow it in a lab, we fill the incubator with carbon dioxide. It hates oxygen. If if it liked oxygen, it’d be a very different threat.
If I were really worried about pepper-vodka botulism (and I’m not), I wouldn’t seal all the air out. I’d make sure there was some airspace, and shake the bottle every couple of weeks to aerate it.