Nobody is debating that a shitty diet may increase your risk for cancer. But a good diet will NOT prevent or cure cancer.
I know the message you're trying to get across is "don't dismiss traditional treatments like chemo" and I agree 100% but the statement I quoted is inaccurate.
Can dietary changes CURE cancer?
I don't know, so I definitely wouldn't recommend relying exclusively on dietary changes and ignoring the medical options you have at your disposal.
If you are diagnosed with cancer, the treatment your doctor recommends should be your #1 priority.
But do dietary changes have a role in the PREVENTION of cancer and recurrence?
In my opinion, there's overwhelming evidence that suggests they do.
I consider legitimate sources like Johns Hopkins Medical to be much more reputable than the link posted in the OP
I agree that sources like Johns Hopkins Medical are reliable and for that reason, this post is based on data from their websites.
According to them:
"There are no food or dietary supplements that will act as “magic bullets” to prevent breast cancer from returning. National Cancer Institute guidelines for cancer prevention can be used to decrease the chance of a breast cancer recurrence. "
Source
Another quote:
"Dr. Silvia Franceschi of the Centro di Riferimento Oncologico in Aviano and colleagues compared the diets of 4,522 patients with breast, colon or rectal cancer with 5,155 healthy control participants. Writing in the journal Epidemiology, they noted that those who consumed the highest amount of raw vegetables—about 12 servings per week—had a 15 percent reduction in breast cancer risk, a 26 percent risk reduction for colon cancer, and a 16 percent risk reduction for rectal cancer when compared with those who consumed only 4 servings of raw vegetables per week. "
Source
The first quote refers to the role your diet can have in decreasing the chance of a cancer recurrence and the second quote refers to the role your diet can have in decreasing the risk of getting cancer.
So again:
Can dietary changes cure cancer?
We don't know, so dietary changes should definitely not replace cancer therapy.
Can dietary changes help prevent cancer?
Yes (quote #2).
Can dietary changes help prevent recurrences?
Yes (quote #1).