Herbs and garlic under oil
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Why oil makes it worse rather than better
People reach for oil because it feels preservative, and it is the opposite. Oil keeps air out, and the organism in question grows where there is no air. Extension guidance states it plainly: when the spores are surrounded by oil an oxygen-free environment is created that encourages their growth at room temperature.
The oil is not the problem; the solid is
A plain oil with nothing in it is not a botulism risk, because there is nothing in it to carry the spores or to support growth. The hazard arrives with the botanical, the garlic clove, the chili or the piece of vegetable, and it arrives whether the solid is still in the bottle or was strained out after sitting in it.
It is invisible
There is no reliable appearance, smell or taste that tells you an oil is affected. That is the whole reason this is handled by a control applied in advance rather than by inspection afterwards, and it is why a maker cannot reason from the fact that nobody has got ill yet.
Which is why 21 CFR 114 reaches this product
Part 114 exists to set out how foods are manufactured and packed so as to prevent conditions in which the organism can grow. A commercially produced infused oil carrying a low-acid ingredient is acidified for that reason, and that acidification is a process control rather than a flavoring decision.
What this means if you want to sell one
Treat it as a product with a process behind it. That means a documented method, a conversation with your state and with a process authority, and an expectation that this is not a cottage food product. Nothing on this page is a determination that any particular method is adequate.