Unfortunately, this is just a special case of a much more troublesome problem: Although plain old laboratory mice do get cancer, they may well do so via very different mechanisms from humans.

A mouse weighs 20 grams. I weigh somewhere around 100kg. So I consist of approximately 5000 times more cells than a mouse does.

The longest-lived mouse in recorded history [1] lived just over 5 years. Most mice die of old age in a couple of years. The oldest humans live to be over 100. Thus, my cell lines will undergo somewhere between 20 and 50 more cell divisions than a cell in a living mouse. [2]

What this means is that human cells have to be much better designed to resist cancer than mouse cells. If humans were no more cancer-resistant than mice we'd all be getting cancer as infants. And evolution hasn't bothered to design mice that will resist cancer for fifty years, because no mouse has ever had a chance to live to be fifty.

So while many of the basic facts of cancer are similar in mice and in humans, eventually the details are bound to diverge. This is an uncomfortable fact for researchers.

This also means that, while it's great for the mole rats that they don't get cancer, that doesn't mean they're somehow more immune to cancer than the average human. Even though mole rats are legendary for their longevity -- they can live into their twenties [3] -- the average human has to be less cancer-prone than a mole rat just to get through puberty without needing chemotherapy.

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[1] Google: "Methuselah Mouse Prize"

[2] This is a really simplistic calculation: Among other things, we're neglecting the fact that mice have a rather different metabolic rate from humans, and that different kinds of cells divide at different rates.

[3] Metabolism again: One reason that mole rats are thought to live so long is that they have very slow metabolic rates. Which probably also affects their susceptibility to cancer.