I am aware of young earth creationist claims that all oil is abiogenic. There are certainly abiogenic processes which can produce oil, but it has also been shown that the decay of organic matter can produce it as well. The artificial acceleration of this process is called thermal depolymerization and is a proposed method of converting organic waste into usable fuel. So necessarily, at least some of the oil in the ground came from the decomposition of dead organisms.

However, the deeper problem with their claims is that they are based on the assumption that Christianity is true, when it provably isn't. Likewise with their frequent claims to have found the remains of Noah's Ark, or human footprints inside of dinosaur footprints, to name a few of their documented hoaxes.