Like many of the commenters here, I have been working out, primarily aerobically, for over 30 years, so feel get a certain amount of 'feel good' emotions from reading this, but almost immediately wanted to say, yes, but strength training helps with the quality of life and maintaining function.
Sincerely, I have a strong bias against the world of strength training, being so gender-lopsided, too much inhabited by traditional men, but my aerobic work, when I am not including strength training into my routine, includes activities that require power and strength, the cross country ski machine and the rowing machine, respectively.
In the end, we likely get some benefits more from aerobic activity, and some aspects better from strength training, but in the end, both matter if one wants to maintain long-term well-being.
Why do so many people have problems with reports on new studies? Why do they take each one in isolation, and not form a complete picture? This article is not claiming to be an exhaustive review of all the available literature but is simply reporting on one study with some ancillary interviews. As a NY Times reader, you are likely well-informed and have read many, many articles touting the fitness benefits of one thing or another. What anyone needs to do is just fit it within all the prior reading, and understand that studies might seem to contradict each other, but that is only normal, given publication biases and statistical distributions. No single study is conclusive or exhaustive, so one needs to understand the totality of information, not just the latest article.
@samusic - They did this as a controlled study, checking levels beforehand, then randomly assigning the subjects into one of three groups. That said, the effects of aerobic and strength activity might be different in older or younger populations, or those that are already fit.