Take for example the Zen koan: "Why did Bodhidharma come to China?" "The cypress in the courtyard." (referring to the tree growing in the center of their monastery.) Zen is a very Japanese version of Chen Buddhism, which was in turn a very Taoist free wheeling version of Buddhism from India, which used existing Indian mythology. Zen Buddhists is very formal and ritual focused, and their koans mostly being about a Chen Buddhist monk who spent his little money on alcohol in the nearby town rather than food.
The Tibetan monk Chögyam Trungpa famously said Buddhism would come to the West as psychology. Who cares who's right and who's wrong, as long as it helps you see the cypress in the courtyard?