I'm Swiss and I volunteer for an organisation called Digital Society Switzerland. Although much smaller (and less powerful) we are similar to what the EFF is doing but on a national level.
I can only confirm your doubts about the "Swiss privacy laws". The current laws in Switzerland are very week (at least compared to the GDPR) and it has powerful surveillance laws in place (6 months data retention for telecommunication data, mass surveillance of internet traffic entering and leaving the country). If at all, being based in Switzerland as a privacy friendly company is rather a risk than giving you a "badge of honor".
I can only speculate where this myth and reputation of "Swiss privacy laws" is coming from. I guess it is related to the bank secret we had in place for a long time: It allowed you to own a bank account anonymously. While many states (especially the US) protested strongly (and for good reasons), it gave Switzerland an aura of discretion.
[1]: https://apps.apple.com/us/app/xsearch-for-safari/id157990206...