Yes. AND no.
=== Why it's sometimes yes… ===
Genetic variations that increase a person's risk of cancer can be completely novel and embedded in their genome. A few thoughts as to factors that make me think a patient might have a genetic link:
- There is no history of the patient's family having cancer.
- They lead a lifestyle free of smoking, excessive sunbathing, and other behaviors that put them at greater risk of cancer.
- They develop a cancer relatively unexpected based on their gender/race/age/etc. (depending on the type of cancer, obviously; some strike all demographics but often there are certain populations at greater risk).
- I think you get the idea.
These people may have inherent genetic mutations in growth factors, receptors, cell cycle regulators, repair enzymes, and/or a myriad of other components of their cellular machinery that in other people work to limit/support cell growth to what is physiologically appropriate. Is this random evolutionary change? I guess so; every cell when dividing makes a few mistakes in copying its DNA, and these people may have just gotten a bit unlucky in terms of where the mistakes happened in the gametes that came together to give them life.
It's more than chance, though, as oftentimes many people with the same cancer also have the exact same mutation–so there's something else at play outside of randomness; it's likely that these commonalities are locations in the genome particularly susceptible to mutation due to relative exposure. I suspect that research will soon be elucidating the mechanistic explanation.
Something very important to point out is that these people should not be treated as mutants/freaks. While certain decisions regarding their care may require greater consideration, they had no choice in their genes, and it would be a serious breach of ethics to discriminate against them solely based on their genetic make-up. For a Hollywood version of what a world like that might be like, see Gattaca.
=== …and why other times, it's no. ===
There are a multitude of cancers for which a patient may not inherently be at risk, but they more or less "acquire" due to certain choices and/or life events, including but not limited to:
- smoking (lung cancer)
- excessive sun exposure (skin cancer)
- not being vaccinated (cervical cancer, females)
- infection by cancer-linked bacteria/viruses (quite a few)
- exposure to mutagenic chemicals, whether in the workplace, living environment, etc. (again, quite a few)
- etc. 
The idea is that while everyone accumulates some mutations throughout the course of their lifetime, these patients accumulate more than average, and hence, increase the chances that the necessary combination of mutations required for cancer will happen. Furthermore, in the elderly, they may simply have lived long enough to acquire the mutations that work in tandem to form a cancer.
The fact is, in the grand majority of cases, it's some combination of the patient's genetics and life experience. It's nigh impossible to simply pin X as the cause of someone's cancer, and really, I don't think random evolutionary change has too much to do with it–or at the very least, we can't be for certain that it does; while certain mutations such as sickle cell trait have been shown to be advantageous in the context of malarial infection, there has not (as far as I know) been any proof of cancer being advantageous in anything other than accelerating an untimely and tragic death.
Note: this answer not to be taken as medical advice! 🙂
 See Ari Shahdadi's answer to What lifestyle choices can I make to reduce my long-term risk of cancer? for some more thoughts.