Yesterday I heard a radio news item in Britain that studies indicate that cancers can be transmitted via polluted air. Perhaps that came from yesterday's Crick Institute item you referred to. However, that may be linked to "underlying damage already in our DNA which makes us susceptible to cancer under certain conditions" (otherwise everybody breathing in such polluted air would get cancer, for no other reason.)
A possible generational link related to "mutations present in our cells from birth that likely shave years off a person's life" is worth exploring with regard to "original sin" and I hope to combine all those elements in this answer, if you can bear with me.
Many cancers seem directly linked to selfish, greedy humans - what Christians point to as part of the sin nature we all have, in every generation. The two links below claim that in southern Italy some firms legally obtained government contracts to dispose of toxic industrial waste, including nuclear sludge from Germany, but then disposed of it illegally, on farmland, on the edge of towns and along the coast. The Italian Senate then investigated a possible link between this and almost 50% of tumours found in the inhabitants of several towns around Naples. A super-grass apparently told police how the Caselesi clan ran "a military-style operation" to dump this material by the millions of tons.
See http://www.nydailynews.com/news/world/mafia-dumping-toxic-waste-blamed-high-cancer-rates-article-1.1505218 & http://www.dailymail.co.uk/news/article-2483484/Toxic-nuclear-waste-dumped-illegally-Mafia-blamed-surge-cancers-southern-Italy.html
"The wonder of DNA is that it deals with organized information. Randomly formed
information DNA molecules would have no information stored within
them. They would be blank media. They could contribute nothing towards
life-processes. It is not the chemistry of DNA that underwrites life
but the information stored in the DNA - information encoded by the
meaningful sequence of base pairs and which spells out instructions
that the living cell can read, translate and use. Life, therefore,
consists not in molecular chemistry but in the information stored by
the molecular chemistry." Who Made God? Searching for a theory of
everything, Edgar Andrews, chapter 13 & pp 244-246 (EP Books 2009)
Link this now to chromosomes and telomers which directly relate to physical benefits and living longer. Sources, http://en.wikipedia.org/wiki/Telomere#Shortening & http://www.yourgenome.org/facts/what-is-a-telomere :
A telomere is a region of repetitive nucleotide sequences at each end of a chromosome, which protects the end of the chromosome from deterioration or from fusion with neighboring chromosomes. In humans, average telomere length declines from about 11 kilobases at birth to less than four kilobases in old age, with average rate of decline being greater in men than in women. Telomere shortening is associated with aging, mortality and aging-related diseases. In 2003 Richard Cawthon discovered that those with longer telomeres lead longer lives than those with short telomeres.
Telomerase is also found in high levels of cancer cells. This enables cancer cells to be immortal and continue replicating themselves. If telomerase activity was switched off in cancer cells, their telomeres whould shorten until they reached a 'critical length'. This would prevent the cancer cells from dividing uncontrollably to form tumours. Blocking telomerase activity could affect cells where tolomerase activity is important, such as sperm, eggs, platelets and immune cells.
Few would say that those "scientific findings support the concept of inbred sin being passed from generation to generation" - certainly scientists would not say that because science can say absolutely nothing about sin. However, for those who take the biblical statements about all humans having sinned, death being their 'wages' for that (Romans 3:23 & 5:12 & 6:23 & 7:5), modern scientific discoveries about DNA, cancer, and the inevitability of death make real sense and provide support for such theology (albeit unwitting support).