I found out about this recently while fact-checking some guy who was trying to bring woolly mammoths back from the dead. He cited elephants' resistance to cancer as a justification for the research. "They have so many cells, but they don't get cancer!" Sounded like junk science, like the myth about sharks.
So it does make some sense ... if there is some small chance that a random cell will go crazy, having more cells would make anti-cancer apparatus advantageous. But mice get cancer too, right? The irresistibly-titled Splenda Reduces Cancer Rates In Some Mice reminds me that science is hard and suggests cancer rates over 60% are typical in mice. What's the smallest animal that gets cancer? When a single-celled organism multiplies as rapidly as possible, it's business as usual.
Pachyderm is a funny word. I guessed that it meant "rough skin" but was off: "mid 19th century: from French pachyderme, from Greek pakhudermos, from pakhus ‘thick’ + derma ‘skin.’" It refers to "a very large mammal with thick skin, especially an elephant, rhinoceros, or hippopotamus."