You would only connect to the network through people to whom you have extended some amount of credit (ie people you would trust with money - be it 0.005 BTC, $500 or 50 kilos of fresh fish... whatever currency and in whatever amount you trust them to pay you back if owed to you) - likewise they are only connected to people they would trust.

Imagine there are two books - one is the BTC order book and the other is the debt record. When you buy bitcoin on the order book, you are paying with the credit granted to you by people who trust you to pay them back - all along a chain until it gets to the BTC seller. If you are owed money by your friends, you can collect it - if you owe money to their friends - they can collect it. You deal with BTC more or less anonymously (address to address) and with fiat on a friend-to-friend basis - if I'm understanding correctly.