It's entirely possible that much of a natural gas was produced from non-organic sources deep within the earth. Oil is different altogether.
We now know that carbon, the fourth most abundant element in the Universe after hydrogen, helium and oxygen, is almost certainly also the fourth most abundant in the planetary system; where it is predominantly in the form of hydrocarbons.
The major planets Jupiter, Saturn, Uranus and Neptune, have large amounts of methane and other hydrocarbon gases in their atmospheres.
Titan, a large satellite of Saturn, has methane and ethane in its atmosphere, and these gases form clouds and behave much like water does in the atmosphere of the Earth. Triton, a large satellite of Neptune, appears to have hydrocarbons mixed with water ices on its surface, as does the outermost planet known at this time, Pluto.
A large fraction of all the asteroids show a surface reflectance closely resembling that of tar, and the comets have hydrocarbons among the gases they emit.
The surface of the core of Comet Halley, recently observed by spacecraft, is most reasonably interpreted as one of tar.
Complex, polycyclic hydrocarbon molecules, similar to those in natural petroleum have been observed to be a prominent component of interplanetary dust grains that currently enter the Earth's upper atmosphere.
While I don't actually have a dog in this fight, since I'm perfectly willing to believe the biological origin of oil...
Still... I do wonder why, if this is a continual process of compressing biomass into oil... where is the halfway made oil?