The notion that money was initially a system of measurement seems like a sound theory to me; a generalized measurement that doesn't require any attribution of wealth on it's own.
"All people, urban as well as rural, tend to lend each other things. They do this even when the benefits to such helpful behavior are not immediately apparent. In small communities, people lend their tools and their time to each other. While they may expect reciprocity in the future, they do not explicitly write a contract to formalize it.
That's an interesting idea, but I can also propose that money evolved from finding ways to get other people to help you:
So little Joey comes over to Gramma Hilary and says "I'm hungry, give me one of your many chickens."
Gramma Hilary says to Joey "Take these buckets to the river and bring me some fresh water, then you can have a chicken."
Joey replies "There's too many buckets, I'll be going back and forth to the river for a long time, but I'm hungry now."
Gramma Hilary says "Tell ya what, you make two trips to the river, and I'll have a chicken all cooked up and ready by the time you're done."
This is barter and trade, a direct exchange without an intermediate currency. And it seems likely to me that these trades existed before money.