It's not really about US citizenship. It's about being subject to US taxation. The IRS has a rather more generous definition of whether you are a "US person" than the INS does.
That said, if you are a legal resident in Switzerland, you should be able to find banking here. If you just step off the plane with a suitcase full of money and walk into a bank, though — I would recommend making it a LARGE suitcase.
FWIW I am not a US citizen but had to fill out an IRS tax form as well when getting a bank account in Switzerland since I was living in the US for 5 years.
