It's really odd that someone would even bring that up.
Switzerland was the last country in the modern world to allow women to vote (1971) - and it was direct democracy that specifically blocked women from voting; a popular plebiscite in 1959 (obviously by men only) specifically prohibited women from enfranchisement. So much for popular progress? In Canada, women could vote in 1917. In Turkey, 1934. Finland, 1906. India, 1950.
The reason that Switzerland will be able to address the Coronavirus pandemic effectively will not be 'direct democracy', it will be wealth. Switzerland became wealthy largely due to a national economic strategy of banking secrecy, asset protection, and of course enabling evasion of taxation and other authorities. At almost 10% of the economy relative to assets under management, the banking sector in Switzerland is indeed substantially larger than other sectors relative to the sectors of other nations [1]. In the US it's 1%. Canada 2%.
Luxembourg, in the last 70-ish years, went from a backwater to even wealthier than Switzerland on a GDP/per-capita basis for similar reasons: it became a tax haven, a policy driven by no less than the outgoing EU Commission head JC Junker who was the PM of Lux. There is no real economy in Monaco, of course, but its high-income status is also derived from its special variation of tax haven. Even Irleand's massive economic renaissance in the last 20 years has largely been driven by asymmetrical tax benefits for large American tech corporations. And of course, Norway's sovereign wealth fund which owns 2% of all public stocks in the world is derived from another existential special economic bit: Oil.
When Corona hits, the 'rich' countries will be the safest (I think the US may possibly be an exception), and I think it will have little to do with their relative forms of government. Aside from their deep social ties to China, I think Singapore, for example, would be one of those ideal 'safe places'.
[1] https://www.statista.com/statistics/267352/size-of-the-banki...