That's an explanation that rests on group selection, which tends not to be taken very seriously by most biologists. Similarly, group selection explanations of why we age are held only by a handful of researchers in the field of aging.
Most biologists in the field of aging hold that aging is the result of the decreased force of natural selection with age. This is somewhat difficult to explain even with diagrams, but I'll try anyway.
Let's imagine three forms of a gene. One causes you to die at the age of eight, another causes you to die at eighty, and the third never causes you to die. We would expect that the form of the gene that causes you to die at eight would be removed from the population very quickly, since anyone who has it will die before they can reproduce and pass it on. In contrast, the gene that causes you to die at eighty will be rather prevalent, since by that age you'll have already passed on your genes to your progeny. In fact, it will probably exist at about the same frequency as the gene that didn't cause you to die at all.
This is the mutation accumulation theory of aging. Because natural selection acts more strongly early in life, we tend to accumulate genes with mutations that are detrimental later in life. There's also a variant called antagonistic pleiotropy, where you have genes that have a beneficial effect early in life having a negative effect in old age.