This sort of explanation for how barter and money came to be is very common. Pretty much every Econ 101 text has a passage early on explaining how in ye olden times people started first bartering and then graduated to using primitive forms of money.
However, there's a good book by the anthropologist David Graeber called Debt: The First 5000 Years, which basically states that all those explanations are pretty much bullshit and not supported by what we know of ancient times. In fact debt systems preceded currency and barter never really happened in the way economists describe. It's a big, complicated book and I can't do it justice here, but if you're interested check out the synopsis on the wikipedia page which I've linked above.
I should note that Graeber, who died recently, was an avowed anarchist and a rather controversial figure. Although one may not agree with a lot of the conclusions he reached, I haven't seen much in the way of criticism of his scholarship on the historical and anthropological record.
