Botulism in oil packed foods
Any low-oxygen low-acid environment with sufficient moisture can lead to the growth of botulism (see page 6 of this USDA guide to canning). Botulism spores are present throughout your kitchen, not just on garlic. To can low-acid foods safely, you need to use a pressure canner for a sufficiently long processing time.
Refrigeration slows down the growth of botulism. The CDC recommends storing garlic or herb infused oils in the fridge for at most 4 days. You should be at least this cautious with your oil-packed fish.