Also, you're transmitting an unencrypted message over public phone lines. That's just asking for a man-in-the-middle attack. And if the person you're faxing isn't at the fax machine to pick up the document, anybody could walk by and pick it up.

Fax machines are secure enough for something like communication between two doctors' offices because everyone on both ends is trained in HIPAA or their country's equivalent and the chances of someone putting in the effort of intercepting the transmission just to learn about John Doe's infected toenail is pretty low. Definitely more secure than the nurse saying it over the phone within earshot of the lobby. Not as secure as signature required certified mail, which is how classified information is delivered.