Flavored oils are usually vegetable oils that have various herbs or other seasoning in them, such as garlic, onion, rosemary, etc. Some are mild and some are strong.
Is there a particular product you are talking about? I use a lot of flavored cooking oils when preparing foods and never had a problem. You are correct when you say that some flavored cooking oils are potent, they are the ones that should be used minimally or the infusion will be too intense, perhaps that is what is has happened with the products you are talking about. I once bought broccoli in cheese sauce, it was in a pouch. I followed the frozen food directions but found that the product had way too much 'liquid type' cheese for me. I did not read the lable so I don't know what the ingredients were. I do remember that it did not taste natural to me. As far as I know this continues to be a very popular product, but I would rather make my own broccoli in cheese sauce.