Over the public network. Via fax that's the PSTN. Via internet that's... the internet. A phone number == A publicly routable IP address.

I think the point was that you still directly depend on a chain of service providers when you use the Internet. You don't free yourself of that.

I think there's an assumed split between infrastructure providers (ISP, PSTN, telco) and service providers (webmail, hosting, etc.) and fax only needs the former.

Ok, so, we're all agreeing on the same thing. The internet method I proposed is the same as faxing, but anything else requires more service providers, machines and steps.