If something flammable is surrounded just by oxygen, I should see flame, right? The object would be even surrounded by more molecules than in the case of gas oxygen. On the youtube I see that people first light-up the objects and then they add oxygen. That means that the things won't oxidize by themselves. Why? Are there materials that would just burn without prior ignition?
Organic material will burn just fine in liquid oxygen. The reason people add liquid oxygen to already burning material instead of soaking the material in LOX and then lighting it is that they are not idiots. If you soak organic material in LOX before lighting it, it becomes a high explosive, called an oxyliquit.