Indeed the ECB would be in excellent position to demand that deposits of Greeks abroad (and that includes Switzerland, where there are close to ~300 billion Euros in Greek deposits and it seems likely that most of that money is undeclared and fishy) be researched.

Recall:

German banks target worried Greeks in Germany

Greeks worried about a debt restructuring or a euro exit increasingly transfer their money to banks abroad, Bild-Zeitung reports. According to the mass circulation tabloid German banks such a savings bank in Munich have posted signs in their windows advertising in Greek and German that Greek costumers will be advised in Greek. According to the paper €30bn have already been transferred from Greece abroad since the crisis started.

And, while an ongoing Euro-run on the entire country of Greece is going on, the ECB is not saying anything about it. All we get is Lorenzo Bini-Smaghi hyperventilating about the consequences of a Greek debt restructuring (among them, insolvency of the Greek banks) when the deposit run from Greek to German banks, if unchecked, will by itself bring the Greek banks down.

Economics is politics by other means