I didn't think so either, but the AA agent kept showing us the requirements that would come up for us in their system. Is it because it's a different airline that we're flying out of SJU with? Is this stated somewhere definitive that I could show?

Looking at https://www.discoverpuertorico.com/info/travel-guidelines it only states that "Those entering any of the Island’s three open airports, whether on commercial or private aircraft, are required to fill out a Travel Declaration Form on the Puerto Rico Health Department’s online portal, which produces a QR code to proceed."