There is a treaty signed by President Clinton which specifically refers to international treatments of Swiss-Americans. The relevant subject being the protection against double taxation.
TAX CONVENTION WITH SWISS CONFEDERATION
MESSAGE
FROM
THE PRESIDENT OF THE UNITED STATES
TRANSMITTING
CONVENTION BETWEEN THE UNITED STATES OF AMERICA AND
THE SWISS CONFEDERATION FOR THE AVOIDANCE OF DOUBLE
TAXATION WITH RESPECT TO TAXES ON INCOME, SIGNED AT
WASHINGTON, OCTOBER 2, 1996, TOGETHER WITH A PROTOCOL
TO THE CONVENTION
One of the most intriguing portions of this treaty is Article 26, which addresses the question of the transfer of information between the two countries about a citizen of both countries.
Article 26: The Exchange of Information.
http://www.irs.gov/...
As I read it, any information, financial or otherwise, regarding citizens with dual citizenship, is considered 'secret' information.
Obtaining Swiss citizenship could be quite beneficial for a business man, financier or politician with Swiss bank accounts or any other Swiss business enterprise desiring to protect or hide certain information.
I'm not saying this is benefiting Michele Bachmann specifically, but it would be interesting if it turns out the Bachmanns have Swiss holdings or other Swiss investments.