When someone who is represented by an attorney signs a sworn affidavit, the lawyer will often sign his own certification that functions as a "notarization" of the affidavit. It would say something to this effect:
I, Creepy Porn Lawyer, hereby certify that Dingbat Sweatnik came before me on this day (September 25, 2018) and signed the attached affidavit.
Avenatti couldn't do this because he's in California and Sweatnik is in Washington. In fact, he's probably never met her.
So Sweatnik's "declaration under penalty of perjury" is the best they could do in a very short period of time.