Overnighting is similar in that the carrier should provide confirmation that a package has been successfully delivered.
Certified mail is probably a better "someone received it" option, if that is the desired requirement.
Superstition leads to lawyers doing again a thing that worked previously without knowing why it worked or having any understanding that it's actually necessary for any reason. Most of the weird forms of words in legal contracts are a result of this, the court probably doesn't care whether you demand someone "Cease and desist" or just "Stop fucking doing that" but who wants to risk that they do care? Let's just write "Cease and desist" the same as we did on the previous document...
So, she uses Fax because her predecessors used Fax, not because there's an actual "something legal-binding about faxes". Just superstition.
There are superstitious people in every profession, that's what "sync; sync; sync" is all about - it's just that lawyering seems especially prone.
Also, it’s amazing to see she did so much to try to notify them. Yes, not being technical, she couldn’t figure out that security team email, but I wonder why all of the Apple people who were getting signals from her didn’t forward it to that team...