As long as they agree that the ledger is satisfactory, they can use that one to deal with, even if the ledger represents things that don't exist tangibly and only have a unit-representation.
People use a medium of exchange that is not credit all the time. However, this medium of exchange exists. That's the whole point. A thing must exist to be able to be exchanged. Bitcoin doesn't exist so there's nothing to exchange. People in bitcoin community blindly believe Satoshi like he is some kind of God. He wrote in his paper that his system creates coins and the community accepted that without a question. But all that his system does is attaching numbers to addresses. Then the wallet is lying that this number is quantifying "BTC" - a digital thing called Bitcoin. But this thing is non-existent. A guy with "0" attached to his address is not able to show a digital thing in his possession, the same as a guy that has 1,000 attached to his address. The last guy simply creates fictions in his imagination and believes that he owns a valuable digital product, without being able to show it. It's like a mythology. Just like people believed Zeus exists without being able to show it, bitcoin community believes bitcoin exists without being able to show it. They are blind believes in the sacred text that Satoshi wrote. It is literally unbelievable that people believe blindly an anonymous guy ever when they see with their own eyes that no digital product exist in their possession.