A specific critique raised in the press release from IARC is that the study has an

"emphasis on very rare cancers (e.g. osteosarcoma, medulloblastoma) that together make only a small contribution to the total cancer burden."

and that it

"excludes [...] common cancers for which incidence differs substantially between populations and over time."

So it sounds like the generalization hinted at in the abstract shows a bigger misunderstanding of statistics than any in the press release. Would be nice if the paper was not paywalled, so we could actually read it.