1. Yep, so the council didn't make the mistake in the first place. It's their fault if they can't key in a phone number properly. The fact that the receiving end insists on fax is another issue.
2. Email are secure too. Faxes can be read by any Tom, Dick or Harry with no trace of who read them whilst they've been sitting on the machine. At least you can tell who might have read the email whilst it was on the server since the persons will have the right security admin levels so can be traced. Reading an email whilst it's in transit is just bunkum. Yes it can happen but the work involved means it's not worth it. And emails are even more secure with PGP et al.
3. Emails can have delivery notification. A simple request to email back is all thats needed.
4. So it's written. But the original is likely to be digitial so can be emailed, rather than printed, faxed, and then scanned into the receiving end's CRM system (or other data management system). If the original was physical then it can be scanned in. A digital copy is better handled in any kind of office.
5. Email are just as quick as faxes, even quicker sometimes since faxes still go at modem baud rates not broadband speeds.
6. Well we don't know who fucked up. But double checking phone numbers, especially if it's a new contact should be standard procedure.
We are all human, but phonebooks on fax machines and address books in email systems help minimise the mistakes we make.
Finally, if it would be better to punish the stupid person not the council. Not a huge amount, not lose their job, but they should be able to learn from their mistake. The council should be penalised in a non-monetary way (publicity) and the council staff who allowed sloppy procedures to build up should also be punished and allowed to learn from their mistake.