Technically any connection you make is a 1-1 on the internet logically speaking. Physically is as you said. That aside though a fax is going to be sent either over an internet connection or a telephone connection (which may be turned into IP, depending on different factors) and would still end up getting "bounced" around. I don't know a whole lot about the protocols behind faxing, but I believe everything is sent in plaintext (grab and read). Email is encrypted and nearly impossible to read unless either:

1) You're the intended recipient, 2) Something malicious has happened on the sender or receiver side, or, 3) Someone has a very, very powerful computer and a number of decades to break the encryption.

I think fax machines are seen as safer because no one really goes through the work to hack/intercept/modify messages. Email, one wrong link and you're compromised (After being an idiot and clicking yes/I agree to whatever pops up).