What oil retrieved is not a fossil fuel? I've been in the oil industry for almost twenty years and can't think of an example. Of course, you might have a different definition of fossil fuel than I do. I'd be interested to read your thoughts.
noun, Energy.
1. any combustible organic material, as oil, coal, or natural gas, derived from the remains of former life.
The fossil part basically means that if it could form a fossil, it could form a fossil fuel. That being said, the geological constraints required to form fossils and fuels are pretty much mutually exclusive. If the thing fossilized, it is unlikely to have contributed its carbon and hydrogen molecules to fuel. Note that I am not saying that fossil bearing formations can't also serve as hydrocarbon sources.