People have made crazy stories up about "the origin of money" for a long time; Adam Smith makes up a zany story about people agreeing to use chunks of metal to make change for bartering because it's too hard to keep chickens in your wallet when you need to break a sheep[1]...
The notion that people gravitate to metal vs "fractional sheep" is without historical evidence. People in fact, a long time ago, did trade things like IOUs or pieces of broken reeds or sticks[2]. Those sticks acted like IOUs and were often traded around far past the original parties to the contract.
Money is a contract between you, your peer/counterparty, and whatever organization you "trust" to mediate if someone really isn't happy with the outcome of a situation.
Money is, indeed, culture.
[1] https://www.adamsmithworks.org/documents/chapter-iv-of-the-o... [2] https://en.wikipedia.org/wiki/Tally_stick