Hmm...I really don't understand why you think a fax machine result isn't a digital copy that is somehow protected from unauthorized modification. A fax machine does NOT ensure authenticity. That was never the intention with the technology in the first place.
You can forge caller ID, and if good enough, even forge the sending phone number/fax header details. What you couldn't forge is the digital signature created with your actual private key. As your public key is mated to it and only you have the private one.
One could create new keys with your name on them, and 'sign' the document, but it won't authenticate on the receiving end if they already have your real public pgp key.
You could easily send a pdf that you took the time to digitally sign with your public key. ANY modifications to that file when checked against your published and known key will cause it to fail the digital signature check. Any attempt to swapout your signature for theirs will also fail, as your private key isn't known to them and couldn't be used to generate the digital authentication on your behalf.
If you want to take authentication seriously, that's one of the best methods of doing so. Include the fact you signed it with the email where it's attached. The recipient can confirm the digital signature hasn't been faked AND the attachment is what was signed by the real you. Quick and easy these days, too. They only need your legitimate public key; which they would have if you have done prior business with them. As, obviously, you sent it before hand.
If someone attempts to swap out your digital signature for another, it won't pass authentication because your private key isn't something anyone else would normally have and your signature is based on that key only. YOUR public key can be used to verify it, because it's mated to YOUR private key that only you have. So, your public key (that they do have) will not authenticate the signature if the signature is created by another private key that obviously doesn't belong to you.
And the recipient will know someone went the extra mile to try and pass something off as yours that wasn't actually from you.
If you want to provide authentication for something you sent, sign it with your valid digital signature using PGP. Altering the signature and/or the contents of the message and/or file attachment will fail the authentication when the recipient goes to verify it. Even if they go so far as to create their own public/private key trying to mimick yours, It still won't authenticate as coming from you because it wasn't generated with YOUR private key.