Here's a link to the two studies published in
Science to which the news article refers:
Vascular and Neurogenic Rejuvenation of the Aging Mouse Brain by Young Systemic Factors
http://www.sciencemag.org/content/early/2014/05/02/science.1251141.abstract
Restoring Systemic GDF11 Levels Reverses Age-Related Dysfunction in Mouse Skeletal Muscle
http://www.sciencemag.org/content/early/2014/05/02/science.1251152.abstract
With regard to your question, there are many biological factors that contribute to aging, and damage to DNA is only one of many factors. For example, a comprehensive http://dx.doi.org/10.1016/j.cell.2013.05.039 of research into the biological causes of aging identifies nine factors that contribute to aging: genomic instability, telomere attrition, epigenetic alterations, loss of proteostasis, deregulated nutrient sensing,
mitochondrial dysfunction, cellular senescence, stem cell exhaustion, and altered intercellular communication. There are likely additional factors that we still need to discover.
Each of these factors contribute to aging in different ways. For example, genomic instability and loss of proteostasis contribute to aging-related diseases (cancer, Alzheimer's, Parkinson's, etc.) whereas other facotrs like cellular senescence and stem cell exhaustion contribute to some symptoms of aging like lowered ability to recover from injuries.
The particular types of aging that the young blood treatments seem to be reversing (age-related declines in muscle function and cognitive abilities) seem more related to cellular senesence and stem cell exhaustion than DNA damage. Thus, the young blood may be revering aging by reactivating senescent cells and/or stem cells in the body without addressing other causes of aging like DNA damage or proteostasis.
However, when you mention damage to chromosomes that occurs during DNA replication, it sounds like you are referring to
telomeres, specialized structures at the ends of chromosomes that get eroded with each round of DNA replication. This erosion sets a limit on the number of times cells can divide and contributes to aging. The body, however, contains an enzyme called telomerase capable of extending the telomeres of cells. It's possible that young blood contains signalling factors that can help old cells activate telomerase and extend their telomeres. (For technical reasons, it is unlikely that telomere erosion is contributing to the types of aging examined in the mice studies. Lab mice have unusually long telomeres, such that even mice lacking telomerase can be bred for a couple of generations before telomere erosion starts causing premature aging in the animals.)
Of course, much more research is needed into figuring out the identity of all the rejuvenating factors in young blood and characterizing their effects on cells at the molecular level (which signalling pathways do the factors activate, which genes get turned on and off, etc.), before we can definitively say anything about which causes of aging young blood can reverse and which causes of aging it does not affect.
