Isn't this sort of like asking "Why does getting shot kill some but not other?" It depends on which part of the body was shot, and which part of the DNA was damaged.
The way I read the article was that cancer is caused by deficiencies in the body's repair mechanism. It appears as if some have a more robust mechanism than others, depending on genetics.
My mom had 14 siblings and only one of them got breast cancer (she was a nun and never breastfed which drastically increases a woman’s odds of breast cancer). But prior to that, her mother’s family, which was also large never had a case of cancer. My mom’s siblings also had around 30 kids between them some now in their 60s. There hasn’t been a single case of cancer amongst the kids either. So it’s something like 150 people with only one instance of cancer over the last 3 generations. There is definitely a strong genetic component to this.
Yes, genetics play a big part but my understanding that cancer is influenced by both genetic and environmental factors. It's possible to have similar habits in the family with respect to sun exposure, alcohol consumtion, diets etc..