If mortality age is a normal distribution, you would see someone 125+ years old every now and then even just naturally. And you don't.
By contrast, standard deviation for height is somewher between 2 and 3 inches. If 70 inches is roughly median, 5 standard deviations is not unheard of. That's roughly 85 inches. 7' 2" is not exactly rare in the NBA and there are players a notch even above that--7' 5" is getting pretty rare.
Standard deviation for mortality distribution is about 8 years. If median is 75 years old, 115 shouldn't be that unusual and 123 should pop up occasionally. Yet, 115 is a staggeringly rare age to live to, and 123 is simply unheard of.
Why would all-cause mortality be normally distributed? The causes of death at the low end and high end tend to be different, so I don't see why we would expect them to occur at similar rates.
Erm, that is my point? They're not.
The human body has systems that break down. The immune system, for example, relies on a fixed number of stem cells that eventually die. Once you have zero of them, you're pretty much done. Also, I seem to remember that our ability to replace fat cells also declines with age (probably for similar reasons).
Consequently, outside medical interventions (or lack thereof) aren't really defining human lifetimes.
Life is effectively a mixture model combining two Poisson point process of things that can kill you (roughly, causes of infant mortality and causes of adult mortality)[0]. We've thankfully been able to shift the mixture weight pretty hard away from infant mortality with modern medicine and improved living conditions globally, but we're still linearly chipping away at an exponential problem (because events in Poisson point processes occur with exponential frequency - the most likely time for an event to occur is always, "now", even if the mean is every 79 years).
Even were we to completely eliminate all causes of death except things that can kill a healthy person in under a minute, we'd probably just end up with a prettier (probably a few decades shifted, possibly amplified[1]) Poisson distribution. It probably wouldn't be hugely different than what we have now, either - all the top causes of death have a "quick" option, and it doesn't take much cumulative probability of death to massively increase the probability your life will end before a certain age.
The article may be right that there is no cap to maximal age, but the likelihood of achieving ages greater than those seen may require significant time, even with the current population level, even if we started intervening generically. I would guess it will always be rare that people live to extreme age, even if that age manages to shift up another decade (shifting the average age of death into the high 90s).
[0] The resulting Poisson distribution of deaths is damped and left-skewed because deaths are not independent (saying which is to eliminate significant real-world detail), which is technically a requirement of Poisson point processes.
[1] Life saving measures are also not independent, which could be a significant factor if we could really recover from anything that required more than a minute to die.
My mother and late grandmother both independently voiced that they experienced medical ageism and disrespectful, dismissive treatment by doctors, hospitals, and care providers.
FWIW, USA is ~47th globally in life expectancy.
Regardless, the USA is only a couple years behind and, with the way life expectancy is measured, that's much better explained by inner-city violence than it is by healthcare.