Well, the study was not an RCT, so the authors by necessity argue for the presence of an association, but are technically not claiming a casual relationship (even if the wording does a heavy 'wink wink' at the reader). That, and apparently the findings were not statistically significant.
However, even if there is an association, and it is "causal", given this is not an experimental study, the relationship could well indicate a reverse causal link.
E.g., patients with a higher likelihood of developing colorectal carcinoma may be predisposed to increasing their beef / milk consumption, which then shows in non-tumour tissues. In this light, the association might even demonstrate a protective effect against cancer (or at least its early symptoms).
One can easily find a biologically plausible explanation for this too. One of the early signs of cancer is loss of weight / appetite. It would make sense that people might instinctively turn to more 'umami/flavourful', low-carb/protein-high diets, to stimulate their appetite and combat the weight loss; particularly in terms of muscle mass.
This kind of explanation might also align with your observation on cancer rates in Europe vs South America. (assuming detection rates are similar in the first place).