I am extremely dubious of this result that red meat causes cancer and have been every time it shows up. Recall that for decades we were told saturated fats were terrible for us and that turned out to be false and that salt caused hypertension (it is far more complicated than that).
To point out some problems with typical meat->cancer studies:
inconsistent definitions of meat categories
use of a food surveys that are notoriously inaccurate
confounding variables likely not completely eliminated, e.g. vegetarians might be more health conscious in general
Of course the biggest weakness and the one that make me suspicious of nutrition science in general is the reliance on epidemiological studies. This just looks at correlations between variables and provides little evidence of causation. It is also very vulnerable to confounding variables problem above.
Furthermore, the mechanisms by which it cause cancer are suspect. One theory I have heard is that certain foreign substances in red meat cause an autoimmune response and the resulting inflammation eventually leads to cell damage and cancer. However, inflammation is a natural process (you cause inflammation when you exercise for instance), so just going inflammation=bad is oversimplifying the case.
Also the statement says that pan frying meats may cause carcinogens to be created, but
Lee, Sang-Ah, et al. "Animal origin foods and colorectal cancer risk: a report from the Shanghai Women's Health Study." Nutrition and cancer 61.2 (2009): 194-205.
found that stir-frying had no carcinogenic risks.
I think the processed meats result is probably true and you should cut your consumption of them.
I guess in the end, just recall that everything causes
cancer.