Physician here. I think I can provide some clarification for what is going on here. I just read the article the WHO is addressing and this is a line from the final paragraph:
Our analysis shows that stochastic effects associated with DNA replication contribute in a substantial way to human cancer incidence in the United States.
First, the terminology is important to understand. In medicine, "stochastic" is in contrast to "deterministic" which describe the occurences of pathology based on a risk factor. In a "stochastic" model, if you receive 10 severe sun burns then your chances of getting a skin cancer go up over someone who only received 1 severe sun burn, but are by no means certain or even that your cancer will be more severe... simply an increase in probability. In a "deterministic" model, if you receive 5 Grays of radiation then you will have less severe symptoms than someone who received 50 Grays of radiation and for the most part, your symptoms will be certain and predictable.
Now you need to have one element of cancer biology under your belt:
http://en.wikipedia.org/wiki/Carcinogenesis
This basically says that as cells divide, errors are propagated through their progeny until there is a proverbial 'straw that breaks the camel's back' and the cell becomes cancerous.
In summary, that line from the final paragraph is basically saying that cells that divide more rapidly in the human body are more likely to become cancer. Well, yeah of course!
We have known this for a long time but what this paper did is sort cancers into two groups, one that is primarily stochastic and one that is primarily deterministic. The result appears impressive because they have a lot of cancers on the stochastic side... stating that their incidence is more predicted by cell division rather than the deterministic, preventable factors.
But as the WHO correctly stated, they are incorrectly analyzing this data as described in this paragraph:
These include the emphasis on very rare cancers (e.g. osteosarcoma, medulloblastoma) that together make only a small contribution to the total cancer burden. The report also excludes, because of the lack of data, common cancers for which incidence differs substantially between populations and over time. The latter category includes some of the most frequent cancers worldwide, for example those of the stomach, cervix, and breast, each known to be associated with infections or lifestyle and environmental factors.
The cancers grouped into the stochastic side overall make up a tiny percentage of all cancers and so by number/%/incidence, the deterministic side would be enormous if graphed appropriately. For example, their most 'stochastic' cancer is pancreatic islet cell which only has 2500 cases/year in the US vs their 'lung smokers' cancer which has >220,000 cases/year.
I mean they seem almost willfully blind to their incorrect conclusion. Environmental factors are HUGE and the cancers caused independent of those would not benefit from screening and environmental risk reduction--a fact we already know!
As a last note, the 'most' deterministic cancers--inherited types--have to be agressively treated with screening, prophylactic measures and environmental exposure risk reduction, etc. You can read about a couple of the deterministic cancers they mention in this paper:
http://en.wikipedia.org/wiki/Familial_adenomatous_polyposis
http://en.wikipedia.org/wiki/Lynch_syndrome