Do VPN providers really operate under single jurisdiction, even though their servers are located in many different countries?

Question

For example, ProtonVPN claims in many places (e.g. Transparency Report, Terms and Conditions, Privacy Policy) that their service operates "under Swiss law", which, among other things (based on their claims), allows them not to save connection logs.

I would understand the logic of such claims, if all their servers were physically located in Switzerland. E.g. user from USA connects to VPN server in Switzerland, then if VPN provider asked (e.g. by court order) to reveal logs it can simply state: "under Swiss law, we are not obligated to save connection logs".

But when user connects to a VPN server physically located in USA but owned by company based in Switzerland, wouldn't the US law be applied in this case (concerning saving connection logs and all the other things), regardless of where company's headquarters are?

Answer 1

But when user connects to a VPN server physically located in USA but owned by company based in Switzerland, wouldn't the US law be applied in this case (concerning saving connection logs and all the other things), regardless of where company's headquarters are?

The US law could well be applied if the VPN provider was challenged in a US court, or served a secret government subpoena. But until that happens and becomes publicly known they can keep claiming whatever to keep sales up.

Same applies to any other country where their servers are.