They didn't say aging stops, but rather the death rates stop rising further after a time, which means that a 90 year old is as likely not to make it to 91 as a 99 year old would be not to make it to a 100.
But by then the rate of death per year is high enough that it doesn't matter much, and within a few such years such a person will be very likely dead due to the cumulative probability of death over several years.
Ok. Age-related death rates converging asymptotically is a known fact since at least 1939. P(death) was estimated to converge to about 0.439 per annum for women and 0.544 for men. That's a 99% chance to die after 8 years for a woman.
I'm not sure this translates into a cessation of aging. Even if P(death) was a hundredth of that, people would still die over time. They would just not die as fast as they do now. What is the definition of aging there anyway? For me, I'd say an intrinsic biological tendency to die over time does not qualify as being freed from aging.
http://longevity-science.org/Greenwood-Human-Biology-1939.pdf