I think one way of looking at this is that humans are generally embedded in larger contexts, because we always come in communities. (The exceptions are, broadly speaking, historically uninteresting.) So it isn't just that Alice and Bob are sitting there at this isolated moment when Alice has grain and trying to work out if it's worth asking Bob, whom she has never met before, to trade the grain for a future favor. Alice and Bob know each other, and are embedded in a community. They have access to a reasonable approximation of each other's reputation. Alice knows whether or not Bob tends to default on his debts. Alice can make Bob pay for defaulting with his reputation, which can theoretically become so bad that nobody wants to trade with him, which in many historical circumstances may be a literal death sentence. (We are very wealthy, and casually trade with many strangers, and have a hard time internalizing the world they lived in.)
Attempts to model Alice and Bob's interactions as if they are strangers meeting for the first time, who generally expect to never see each other again, may be of some mathematical utility but won't explain the real world very well.
So, it's neither a formal debt in anything like the modern sense, but neither is it "maybe you'll repay me in the future"; there's not total assurance, but in the community context there's much higher assurance of future repayment than that.
What these cultures had, according to Graeber, were essentially ledgers for keeping track of debt.
If you don't repay your social debts, you're going to find yourself getting a lot less favors done for you, and having a lot less friends in general.
This is an oversimplification but gives you the gist of the book's argument. So yes, it agrees that money is a relatively late development and trade existed before it and was largely barter-based but only when strangers or rival groups traded, but the central argument is that debt (basically) came first rather than last, and effectively precedes money, which is more a tool of debt than debt is a tool of money, if you will.