This study appears to bear that out. What they found is that vitamin C, both in vitro and in a mouse model, allowed the tumour cells to survive by protecting the mitochondria. That makes a great deal of sense because mitochondria are a "gateway" for death signals and anything that preserves mitochondrial function typically helps keep the cell alive.
Sounds simple but isn't, there is also the possibility that in some cancers activating certain functions of mitochondria, in particular the release of pro-apoptotic factors, can activate cell death pathways. Additionally some studies have found that high doses of intravenous vitamin C can be effective in killing cancer cells. What a dilemma, take antioxidants to try and prevent healthy cells from chemotherapy damage and run the risk of helping the cancer cells to survive.
Ironically part of the problem here lies in the singular tense word "cancer". Even cancer originating in the same body tissue of the same person may be a different type of cancer. Because of this, strategies to target cancer are never going to constitute a single magic bullet, we will always have to tailor the strategy to the specific type of cell present in the tumour. So in some instances antioxidants may not present a problem because in some cancers the mitochondria are disabled or poorly functioning. In other cancers improving mitochondrial function may induce death signals like APAF1, BAX, BAD. Even then it can become complicated because some cancers have high expression of the small heat shock protein, hsp27. This protein can bind these death signals so preventing cell death.
Just to confuse the picture there is clinical evidence that the intravenous administration of vitamin C can kill cancer cells. The reasons behind this are unclear but it is known that high doses of vitamin C, particularly in the presence of free iron, can drive oxidative processes via Haber-Weiss and Fenton reactions, thereby inducing cell death. To achieve such high doses though intravenous injection is required because the body will not absorb large amounts of vitamin C orally. Hence all those people taking large doses of oral vitamin C are wasting their money. For a look at the use of intravenous vitamin C read of this article. A short comment in the Canadian Medical Journal puts forward the case for using intravenous vitamin C in cancer therapy.
It is never going to be easy! So when you see all those internet advertisements proclaiming a universal cure for cancer don't go there. It simply isn't true, each type of cancer requires a different strategy. That is why the success in cancer treatments is not uniform. Great strides have been made in treating some cancers while other types, for example brain tumours, virtually no progress has been made in 20 years. In all this remember what Mencken once wrote:
"For every human problem, there is a neat, simple solution; and it is