The influence of the Olmec on the later groups cannot be ignored. Of course, it makes a lot of sense that three geographically and historically close civilizations that traded with each other would have a considerable effect between them. As with most religious practices around the world throughout time, a new civilization borrows ideas from an older or established one in order to ease the transition for believers who wish to fit into the new way of life more fully.
Luckily, the Aztec and Mayan civilizations had much more in-depth information about the people they traded with and what they saw them in general. Besides rock carvings that form the more primitive form of record-keeping, these two later groups of people had books. If the Olmec ever had such a thing, they have been lost forever.