Absolutely. But when you inflate your own currency, it is you who have to deal with the consequences. If you inflate everyone's currency you reap all the benefits and leave everybody else with the burden of the consequences.
Inflation isn't controlled by the ECB. Money is created when banks loan out money. Whether that be to people, companies, or governments (municipalities and so on). That's where all money comes from and how the currency is inflated.
The country which by legislation or by other means makes it easier for banks to lend out money will benefit their own citizens and companies, since they get to be the first spenders of newly created money before it reduces in value. That's how national governments can use inflation for their own benefit within a common currency system. But no government involvement is necessary. If a group of people (in this case the Greeks) are willing to take on extraordinary amounts of debts compared to other groups, then we have the same results.
Remember that all money which was borrowed in the European "debt crisis" went somewhere before the loans couldn't be paid. Somebody benefitted, and the idiots were left to pay.
