The ECB is the central bank not for a single sovereign country but for 17 sovereign countries. In this setting there is no one-to-one correspondence between the ultimate owners of the central bank and the ultimate owners of each government’s budget.
The fact that the ECB has to serve 17 sovereigns also means that the tool kit of monetary policy is more limited than for a single-country central bank. It follows that the moral hazard considerations related to central bank actions in a monetary union are very different in comparison to a single-country central bank.