It seems that the BALLOT OATH sheet that you might find with your mail by vote Ballot is one that you only need to fill out if you indeed FAX your ballot.
Better check the rest of the Internet to figure out if this is true.
Writing it here, since the paper that says BALLOT OATH and LARC20210001 INST MILOS E starts the explanation with:
In choosing to return your ballot by fax or mail, …
The “or mail” made me believe that even if I mail in the bail I would need to fill it out. While the instructions that came with the ballot did not mention that form to be included.
But, as I said: better check the rest of the Internet for better and more substantial information on this. Why the form is non-conclusive? Well. Lawyers. Not enough of them… [joke].