There is an expectation from the Swiss authorities that efforts are made to comply with the rules and not game the system. I would follow the financial requirements spelled out by the ETH/UZ:
"Evidence of sufficient financial means:
You must produce evidence of sufficient financial means to support your stay in Switzerland.
You can do this by providing bank statements and/or scholarship awards. The Canton of Zurich Migration Office requires confirmation from a bank with a branch in Switzerland (it doesn’t have to be a Swiss bank, but a foreign bank with a branch in Switzerland 6).
As a rule, you should be able to provide evidence of having CHF 21'000 at the beginning of each year of your studies.
You yourself must be the account holder and the account balance must be shown in Swiss Francs, Euros or US Dollars either on the bank statement or in an additional letter from the bank. Please note: Even big and internationally well-known banks are not accepted if they do not have a branch in Switzerland. Examples of accepted banks are: Citibank, HSBC, Deutsche Bank, etc. Supporting letters of parents are not accepted.
Alternatively, you can hand in a so-called “guarantee declaration”.7
6 Please check https://www.finma.ch/en/~/media/finm.../beh.pdf?la=en
for a list of banks with branches in Switzerland.
7 This means that a solvent person living in Switzerland (Swiss citizen or foreigner with B or C permit) underwrites to cover the costs of up to CHF 21’000.
- for your living expenses, including accidents and illness, in addition to your return trip. The appropriate form is sent to your home address by the Migration Office of the Canton of Zurich (once the y have received your visa application)." https://www.ethz.ch/content/dam/ethz...-master-en.pdf