I don't blame them for not accepting faxes because it may keep the employees from downloading viruses in anonymous attachments which may be open by mistake by an unsuspecting employees.
That only needs to happen to you once for someone to rethink faxing rather than electronic documents.
Might want to see what protocols you can put into place that would prevent another incident. Especially if you are contemplating the extreme of totally not accepting what is the more common form of communication now.
Totally doing away with email and only accepting faxes would kill my business, so that isn't really an acceptable answer for me. For others, it might be best. It would really depend on who your clientele is. I have never had someone ask for a fax number, so I doubt I have any customers that require that form of communication.
I can understand to a point that argument above, but by putting in better controls that would help mitigate what goes on. Keep mission critical computers away from the internet and keep computers that are on the internet away from the local network.
Make sure all computers have anti virus software to run on incoming files before they get into the local network. That would mean antivirus software no matter what PC OS you run. Yes, Linux and Mac can also get malware as well. Statistically not as likely for a variety of reasons, but they can still get it or if nothing else be a typhoid Mary and affect your Windows machines if they have access to the local network that is run with Windows machines.
Another bad habit that I see is that typically Windows users run as full admin all the time. Windows machines are kinda clunky compare to Unix type machines. Even if there is only one user for a Windows rig, you need to setup 2 accounts. One admin with a very strong password and then your standard user account that you do everything through. Most Windows users only run in one account with no password. That doesn't help matters.