Yeah, you’re right - it’s SMTP not NNTP. Considering that back in the day I used to telnet to port 25 of my uni’s server to send e-mails portraying as one of my teachers to take the piss of my friends and hence knew at least some of the protocol, I must be getting old to confuse the acronyms.
But yeah, the main point is not the network being “public” (in the sense that anybody can access it) it’s that - as I explained but you seemed to have missed - the intermediate hops for an e-mail travelling on the internet can be owned by just about anybody and, worse, not necessarilly in your country working under local laws - routing will often send things around in quite unexpected tours on a physical sense depending on network topology - whilst the nodes the fax data travels on a phone network are generally owned by just 1 company or 2 (the latter in countries with multiple landline providers if you send it from a phone in one to the phone in another, as the network topology is much simpler and all providers connect to each other directly).
If your data goes over at most only 2 networks owned by very specific companies it is inherently safer from eavesdropping that if it goes over an unknown number of networks owned by an unknow number of companies. This is not the same as saying it’s “safe” - it’s just one relative to the other, rather than an endorsment of faxing.
Also there are usually laws around eavesdropping on phone calls, from the old days, whilst it’s the Wild West out there when it comes to those operating intermediate nodes eavesdropping on e-mails.
Frankly, if you can’t send the data encrypted, then faxing is probably safer from a privacy point of view (it would take a crooked telecoms operator risking their license, a Court Order or physical access to eavesdrop on it), but if encrypted e-mail is safer at least content-wise, though as I pointed out plain e-mail with unencrypted headers leaks meta data even if the contents is encrypted.