They have been able to give him pieces of money because they themselves had rendered services.
In this second part, Frédéric Bastiat explores what he calls the “Progress in Exchange”; how we went from barter between two parties to circular barter and then to non-simultaneous exchanges in neither value, time or space (sale and purchase being separate transactions) thanks to the introduction of money.
What I like in today’s quote is that he underlines that the value of money is linked to the exchanges that are made. While metallic money, which was in use at the time, tends to reduce our understanding of the role of money because of the intrinsic value it was supposed to have, Bastiat understood that what gives value to money is the service that is represented. I shall not say that he saw the era of fiat money come but it is possible that he would have accepted it for what it is, viz. a symbol of trust between buyers and sellers towards the stability of its value in time and its acceptance by others.
I would go even further in thinking that he would have been skeptical towards crypto-scams like bitcoin, which do not really get their value from rendered services (even if they exist in mining) but from the way they are made scarce through the algorithms defining their availability to users. If demand grows faster than their creation, their price increases (and vice-versa), independently from the services offered by the sellers or the miners.