Central banks act as clearinghouses for payments between regular banks. The fact that each bank has an account and reserves at the central banks allows them to trust each other and credit each other payments even if there's a delay in money actually changing hands.

In the case of cross-border banking you need central banks to clear payments with each other. The ECB might act as a clearinghouse for payments among national central banks. If that is the case and the ECB refused to clear payments with the Italian Central bank, the Italian monetary system might become cut off from the rest of the EU.

At least as I understand the situation.

Of all the ways of organizing banking, the worst is the one we have today — Mervyn King, 25 October 2010