Tortoises were the first to come to mind for me. Later in the article, it does state that it's not just size but metabolism that figures into this correlation.

That being said. The article states that this relationship governs "all life" but only gives data for plants. Even there, "some variation, but not a lot" is an extremely generous representation. For the same mass, a difference in mortality rate could be 10^3 or more if I'm reading the graph correctly. While the relationship might roughly follow a trend, I wouldn't call that "not a lot" of variation. It's interesting, but I think the authors are overselling the relationship.

Further, it can't just be metabolism. It is unlikely that it's simply the metabolism of some tortoises, lobsters, and hydras that causes them to not actually age. It's not that they just have extra long lifespans, their death rates do not increase with age.

I was thinking about parrots. Not especially heavy, and can live 50-100 years.

What about dinosaurs? What about that "hobbit" species (Homo floresiensi)?