One way is to add a character, like the letter "F" in front of any fax
number so that Outlook does not recognize it as a phone number.

Right. That's what it's supposed to do.
Outlook considers fax numbers to be valid electronic addresses, since there
are many client- and server-based components that can use such addresses.

One method to hide fax numbers from the address book is to prefix the fax
number with one or more letters (maybe B for business fax, H for home, O for
other). If the fax number begins with a letter, Outlook won't show it in the
address book.

There are a couple of utilities that can help you hide fax numbers from the
address book. See:
http://www.rsoutlook.com/us/rshifa.htm
http://www.sperrysoftware.com/Outlook_Solutions.htm (Hide Fax Numbers)
http://www.mapilab.com/outlook/toolbox/

Another way to avoid having fax numbers appear in the address book is
simply not to enter data in the fax fields. Put fax numbers in some other
(non-phone) fields.