The reality is different from any tale.
Switzerland is currently under a strong attach of EU and US.
EU and US are both trying to have access to list of their citizens with a Swiss bank account and, in very few words, pushing Switzerland to remove the bank secrecy.
Major Swiss bank (UBS and Credit Swiss) have been punished, especially in the US, to help people avoid taxes.
There are still banks (on top of the two mentioned before) that allow non-resident to open banks accounts but some of the initial conditions requested from bestman (Anonymity, my name not on card or bank account) are not applicable with the capitals mentioned by other members.
To have this type of secrecy (numbered account, no name on cards and so on) the capitals requested are over 1MCHF.