Not exactly, because of the way public addresses and private keys work. Anyone can check that the address 1xGibi... holds the declared amount of bitcoins. Only

Not exactly, because of the way public addresses and private keys work. Anyone can check that the address 1xGibi... holds the declared amount of bitcoins. Only someone with the knowledge of private key can transfer them to other address. So you can verify the address and physical integrity of coins before accepting them. You may think of this as of passing around a signed check.