I want to make sure I am understanding this.
Person B wants grass cut-hires person A
Person A wants fruit-cuts grass for Person B, buys fruit from C
Person C-Now has money
So, person B hires A to do something that is an intangible, to the extent that he is getting a service (as opposed to product) and he pays person A for that service.
Person A goes to person C and buys a product from person C.
Now, you want to assume that Persons B and C never have a direct or indirect exchange in their lives’, but the problem here is that they already have had an indirect exchange through person A.
In fact, it is only because of the existence of money that this exchange could have taken place the way that it did. Assuming that person A used all of their earnings from the grass cutting for fruit (essentially meaning they cut grass in exchange for fruit), then without money the barter system would work such that person B would have to take some sort of tangible good (or intangible service) and barter it will person C in exchange for fruit to then use to compensate person A for the grass-cutting job.
Either that, or B would have had to compensate A with some other good that C would accept in exchange for some fruit.
Money sort of balances things out as well, particularly in the individual and private market because people know what they can do with their money other than pay whatever someone else is willing to take for some good. In other words, let’s say that person A is completely without food, in the barter system, people could theoretically collude against person A and make person A perform ridiculously long duties in order to just get enough food to eat. They could do this because they know that person A is completely without food, and thus, food holds more value to A than any amount of labor.
With a currency-based system, though, starving or not, Person A has a little more control because he can demand a certain amount of compensation for his labor. Of course, he will not always get it if other people are asking less or do a better job than he does, but he can at least demand it.
Or, maybe I’m not getting your question…