The reason a lot of dual citizens end up getting identified as U.S. citizens is that it's not just a matter of which passport you present. The FATCA compliance procedures require banks to search through the data they already have, and examine new account applicants, for what are called "indicia of U.S. status." These include:
- identification of an account holder as a U.S. person
- a U.S. place of birth
- a U.S. address
- a U.S. telephone number
- standing instructions to tranfer funds to an account maintained in the United States
- a power of attorney or signatory authority granted to a person with a U.S. address
- a U.S. "in-care-of" or "hold mail" address
The big one here is a U.S. place of birth showing up in your passport (of whatever nationality). Also, for new accounts, you will be asked for your place of birth.
Under certain circumstances the bank also needs to look at "actual knowledge of any relationship manager associated with the account." Translation: If you show up to the branch speaking English with an American accent...
If U.S. indicia are identified, the bank is then required to obtain additional documentation. (For example, they;ll ask for a certificate of loss of nationality to prove that you renounced your citizenship.)
The rules are very well-written and are designed to encompass every conceivable situation and every common method of concealing your citizenship.
For some light bedtime reading: http://fatca.thomsonreuters.com/wp-content/uploads/2012/09/FATCA-FAQ-for-a-Compliance-Officer.pdf