I thought these viruses had reservoirs in common farm animals and that's why they were so hard to eradicate. Is there reason to believe they've disappeared from those populations as well?
Not this strain. From the article: "With circulation of IBV only in humans and no established animal reservoir... The considerable reductions of influenza circulation globally due to COVID-19 may have already precipitated the extinction of the B/Yamagata lineage."
No animal reservoirs that we know of. Big difference.
What else did you think what the origin comment meant? You thought that person is an omniscient god that can inspect the entirety of the animal kingdom at a moments notice and verify there are no animal reservoirs?
The article mentions that the influenza B virus has no known animal reservoir.