The authors collected data on life span, brain weight, and body weight for over 600 mammal species, including carnivores, ungulates, whales and dolphins, rodents, tree shrews, primates, and others.
Despite substantial variation with regard to brain size, body size, and lifespan, only the rodent and primate groups displayed correlations between larger brains and longer lives.
Primates that are long-lived with large brains would have evolved from shorter-lived animals that already had large brains.
Conversely, long-lived rodents with large brains evolved from smaller-brained organisms that already had long lives.
Since these correlations only exist with primates and long-lived rodents, and this correlation is inverted between the two, it implies to me that the correlations are merely accidents of circumstance.