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?