In the US if such a product actually worked, it would be an OTC product, not a Cosmetic. I agree that some less than clear or ethical Marketing campaigns foster the misconception that an oil can grow hair, but it is just that, Marketing.
Rather than making hair growth oil, water based serum is the best option to go for as water penetrates more deeply than oil. Most of the synthetic hair growth actives are water soluble which is a extra advantage of it. None of the oil would give hair growth and moreover now a days, most of the people avoid usage of hair oil.