If I may, I would add that it is (obviously) unheard of computer viruses sent by FAX, whilst - besides the "benign" (if we can call it so) spam - a generic hotel e-mail is bombarded by phishing attempts and more generally "check this attachment (enclosed invoice)" or "booking confirmation check the attached image for credit card number" kind of letters, so, besides the time needed to open the e-mail, the e-mails are anyway a "risk".
The worst that can happen with a FAX is that the "attacker" can make you consume some paper and printer ink.
It's not exactly a virus, but last fall some folks put together a PoC showing how certain fax machines could be compromised over the phone line, and used to gain access to their connected networks. [1]
Yep, IF the FAX is connected to network (some are, some aren't) and I would be surprised (even if the researchers do state that) that a "generic" exploit (meaning ALL brand/model of all-in-ones) is possible (maybe they would need a "library" of similar exploits and test them until they find the "right" one for the given brand/model at the other end).
The worst that can happen with a FAX is that the "attacker" can make you consume some paper and printer ink.