It appears from the wording in the statement that it was the additional DNA testing that unearthed the identity of the 2016 author. But why did it take four years from receiving the 2016 letter until further DNA testing identified the sender, when you consider that the Riverside Police Department have always had their sights set on an individual for the murder of Cheri Jo Bates, who went by the fictitious name of "Bob Barnett"? It isn't beyond the realms of possibility that when the Riverside Police Department received this 2016 communication from somebody alleging he was not the Zodiac Killer or the killer of Cheri Jo Bates, he may very well have been the murderer in the case of Cheri Jo Bates, playing more games with police as he did in 1967. Investigators obviously found the 2016 communication compelling enough to consider it for DNA testing in 2020, rather than just dismiss it as another hoax letter. They must have received many crank communications down the years regarding the murder of Cheri Jo Bates and the associated communications in the case, so what set the 2016 letter apart for the FBI Los Angeles Investigative Genealogy Team to get involved? Or do they routinely DNA every crank letter making claims or admitting some responsibility to the events in 1966 and 1967? I highly doubt it.
All but two of the authenticated and unauthenticated Zodiac letters we know of currently, were mailed to newspapers not police agencies. The letters to a police agency in Northern California from 1969 to 2001 were mailed to the San Jose Police Department on November 21st 1969 (which threatened a widow), and the August 10th 1969 Concerned Citizen card to Sergeant John Lynch of the Vallejo Police Department. But this wasn't a set of letters, or letters designed to keep the investigation going. One way in which the Riverside Police Department could have judged the authenticity of the individual's claims in 2016 would have been to request details of the further hoax letters he mailed to Northern California claiming to be the "Zodiac Killer" and attempting to keep the investigation going. Had Riverside Police Department checked these further claims and verified them, it would have given more credence to this individual that he was a serial hoaxer involved in manufacturing the three Bates letters. These further hoax Zodiac letters and the way they were written and designed could be the key to the confidence displayed in the recent statement from the Riverside Police Department.
The first time it was widely known of the Zodiac Killer connection to the Cheri Jo Bates murder case, was when Paul Avery wrote extensively about this in the San Francisco Chronicle on November 16th 1970 in an article entitled New Evidence in Zodiac Killings. It read "On April 30, 1967, exactly six months after the killing, three stamped letters - addressed to the Press-Enterprise, the police, and cruelly, to the slain girl's father - were dropped into a city mailbox. BATES HAD TO DIE THERE WILL BE MORE was printed in large scrawled letters on each of the notes penciled on pages of lined 3-hole school paper". So any additional hoax letters created to keep the Zodiac investigation going, mailed by the 2016 claimant of the three Bates letters, likely came when he saw the connection between the Riverside and Northern California murders. This article may have been the incentive to project himself into the Zodiac case and mail additional hoax letters to Northern California police agencies. Assuming these further letters were retained, it could have been a simple case of interviewing the 2016 individual and asking him where he mailed these additional letters from (and their content), and cross-checking the postmark to verify his claims. Four months after the Paul Avery article, somebody claiming to be the Zodiac Killer decided to shift his letter writing from the San Francisco Chronicle to the Los Angeles Times, because "they don't bury me on the back pages like some of the others". The author of the March 13th 1971 Los Angeles letter begrudgingly acknowledged the authorities for stumbling across his Riverside activity, adding that there was a hell of a lot more down there. Downtown Los Angeles is about 60 miles west of San Bernardino.