My best guess would be that they are so because they are eusocial.

As I posted in a comment below somewhere, I think it is the complexity of the nervous system that drives a tradeoff with repairable bodies. A brain does not want to have to retrain itself, but the history it stores makes it entropically very energy intensive to maintain. I think this drives most of what we see here: things without complex nervous systems (pyramidal neurons and such) have no disincentive in persisting indefinitely, because their relatively simple nervous system does not take increasing amounts of energy to maintain, and thus they can budget their energy for growing and other evolutionary benefits.

Most mammals have to budget their energy such that they can maintain the state of their brain, and thus have a disincentive for eternal aging: we either need to start forgetting earlier memories, which could potentially be bad, or we have to start paying the energy price of maintaining a very complex system. Energy usage tends to get optimized by evolution, so then, we end up trading off longevity.

Mole rats, however, being eusocial, have a different evolutionary strategy than most mammals. Since the entire colony effectively behaves as a single metaorganism, losing its experienced members is particularly painful if they have valuable institutional memory. Thus, there is stronger evolutionary pressure to pay the cost of maintaining these systems.

(I realize that isn't really what you were commenting about, but it does give a thermodynamic reason for their longevity, but not one simply based on temperature.)

> Thus, there is stronger evolutionary pressure to pay the cost of maintaining these systems.

... which implies that it is biologically possible to maintain them, which implies in turn that aging is a biological trade-off and not a physical inevitability.

Yes, I agree. I guess the question is what is meant by inevitable. The meanings of biological and physical in this instance aren't really all that different, if the biological problem is a limitation of the underlying physics. Ultimately, the scarcity of usable energy is driving this trade-off, which is a physical limitation of the universe. It becomes 'possible' in the sense that a O(n^100) algorithm is 'feasible' (see Arora and Barak, section 1.6.2). If maintaining a youthful state indefinitely increases our energy consumption hundredfold entirely due to the cost of maintaining a low entropy state in a highly complex system, is that really 'possible'? If we have to pay an ever increasing energetic cost to maintain ourselves, it is both a biological trade-off and a physical inevitability.

I was driving at a similar point, but I think this might be a % of available slack in lifespan, which does not discount physical inevitability.

This raises an interesting point. Having said that losing experienced members is particularly painful, I am now thinking about how someone's feeling of meaning in life affects lifespan. Could it perhaps be the case that there is a self regulation mechanism in which perceived usefulness drives the brain/body to try and stay operational longer?

Interesting...that's different, and does not square with the article's premise. It does not sound like that organism is just getting longer life by keeping its cells in the refrigerator. Especially this part:

"Naked mole rats also appear to remain spry and healthy even in the final years of their long lives"

Sounds like they changed the shape of the curve, not merely stretching it out.