That's not how it is described in the FAQ, it refers to currency stored on device, transfers verified by the offline device, and in a private way where the banks and central bank can not look at who made the transfer.
>Offline digital euro payments are instant transfers which could be made without an internet connection, as long as there is physical proximity between the devices of the payer and the payee as it happens with cash now. Users would be able to store digital euros in their device for offline use, below a certain threshold exactly as we do with cash in our wallets. Offline digital euro payments would be validated “peer-to-peer”: the payer and payee would directly verify that the transfer of value between them has effectively happened. Such payments would be used mainly for small payments. Just like cash, the details of your offline payments in digital euro would not be visible to anyone – neither your bank, nor the European Central Bank.