The bizarre morphology of Native American pictographs could have less to do with cultural stylization - or even UFO's - than distorted imagery rendered by hallucinogenic visions. In short, the answer might be pharmacology and not cosmology.
Peoples such as the Ancestral Puebloan were familiar with substances like psilocybin mushrooms, peyote, and datura. Tribal leaders and shamans would induce visions by ingesting these toxic plants. From their bizarre imaginings sprang forth fantastic images of strange worlds and the creatures dwelling there. Believing these visions held portent, what they saw was then recorded into stone glyphs and pottery for posterity.
Of course, without being able to penetrate the thoughts of someone a thousand years removed, it is difficult to say for certain that it wasn't inspired by extraterrestrial visions. Still, it is a unique counterpoint to ponder when one desires a balanced examination of the UFO/EBE enigma.