Historically in Switzerland a minimum of Francs 1 million was required to open an account, however, over the last years many private banks have lowered their entry hurdles to Francs 250,000 for private investors.
It might be not possible for your boss to open a Swiss bank account since he holds Dual Swiss and US Citizenship. He may, under Swiss or US laws, have to renounce one country's citizenship in order to open a Swiss bank account. This might be a result of Tax laws. If he makes money as a US citizen and puts it into a Swiss account which country has jurisdiction for Tax purposes? As a Swiss citizen with a Swiss bank account the US will not be able to see the books. Hence, a trade agreement most likely exists that dual citizenship cannot open a bank account in Switzerland.
Romney has that Swiss Bank Account for that very reason. US law cannot open that account and investigate where and how that money came in and goes out.