It's not clear from the article but animals can generally live quite a bit longer than you'd expect if they continue to grow for their entire life, which is true for some types of fish. Gunk that builds up inside or between cells gets redistributed over larger areas, as do cells that become senescent. And larger size means more space for memory T cells. Those are only some aspects of aging of course.
It might be a matter of cell count still, elephants have many extra copies of p53, one of the main cancer-suppressant genes. We have one copy, elephants have 20. So the linear correlation may still be there if you'd remove those extra copies.
"Peto's paradox is the observation that, at the species level, the incidence of cancer does not appear to correlate with the number of cells in an organism. For example, the incidence of cancer in humans is much higher than the incidence of cancer in whales, despite whales having more cells than humans. If the probability of carcinogenesis were constant across cells, one would expect whales to have a higher incidence of cancer than humans. Peto's paradox is named after English statistician and epidemiologist Richard Peto, who first observed the connection."
It's not consistent across species because different species have different mechanisms for averting tumor growth. But within species (certainly among humans, and I'm pretty sure also among others), more cells means more opportunities for something to go wrong and so more cancer.
