Preserving Peppers in Oil
ANSWER - The peppers may be dry enough after cooking to be safely preserved in oil. But we just can't be sure that the moisture content, which is critical to prevent botulism, is low enough. Recommendations are always conservative in these cases so treat as garlic in oil. Better yet, preserve these items in vinegar or lemon juice. See the link below for more on this topic.
See an update to this answer in this Q&A forum. Search for the word oil, and click on "Prepared vegetables and herbs stored in oil"

