That statement is pretty stupid in general. But for server side software, open source doesn’t help much. Even if you can look at the source, you still need to trust them that that’s what they are running on their servers.
Doesn’t help much in terms of privacy. But still is very important. https://www.gnu.org/philosophy/who-does-that-server-really-serve.html
For a bank or any system you would not have control over anyway, it does not have to be open, only the client software you run on your computer should be. But messaging, document editing (like Google Docs), etc. are personal tasks that could be done via a local program, so a remote program should be give you freedom from it’s provider.
Open source is important for services with end-to-end encryption, because you can make sure the client actually encrypts the outgoing data, is not sending your private key somewhere, and won’t break that security at some point in the future.
Of course this particular service cannot even have end to end encryption in the first place.
I think there is levels of trust.
I am often able to reach of level of trust to believe a company is not straight up lying about the code they are running on their servers.
I am not often able to reach a level of trust to believe a “trust me bro” from a company (especially if that statement is not qualified in a meaningful way).
