Hi Dancho,
I would say a phishing attack would seem the most likely way that the hackers obtained the Twitter credentials and could also explain why the bank knows that no customer/personal data was compromised.
Lately there have been reports of false Twitter notifications. By clicking on the links in these emails you could be infected with a virus or perhaps you might be asked to enter your Twitter credentials. Unwittingly you are not logging in to Twitter but instead providing your Twitter password to phishers. Best security practice: only respond to direct messages and check out new followers by going to the Twitter website.
Deborah Galea, contributor to Email Security Blog: http://blog.policypatrol.com.
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