I agree with almost everything you said. But, botulism is on another level from other foodborne illnesses in that it can much more easily kill an otherwise healthy person. Salmonella, gastroenteritis etc. will make you feel crummy for a little while, but with treatment will generally resolve without permanent consequences. Botulism (or more specifically, a high concentration of botulism toxin from the growth of botulism bacteria) can be much more serious, and you don't have to be an infant or an elderly person for it to kill you.
Obviously the author has had a fine experience with this recipe, and hasn't had any illness or death. Maybe if you thoroughly cook the garlic before it goes into the oil (as this recipe seems to call for) it eliminates the risk. But, I really don't know. And it seems wise to post the warning, in my opinon. Or, at the least, include a warning about the potential risks if the garlic isn't thoroughly cooked (if indeed that is a sufficient process to mitigate the risk).
As to whether someone is likely to use a whole mason jar full of hot sauce in 2-3 days... I love spicy food, but it takes me 6-8 months to get through a big bottle of Sriracha or Tapatio.
I am definitely not trying to be a wet blanket; just trying to present the food safety risks of garlic-in-oil. Like I said, it may be that by cooking the garlic the risk is eliminated, but people should look into that (and thus make sure to thoroughly cook the garlic) before making it.