The obvious objection to almost every study of this sort is that associated with doesn't imply causality, and it could be that some third factor like "propensity to consume highly-processed food products" is responsible for the observed correlation. But from the abstract:

> Associations between sweeteners and cancer incidence were assessed by Cox proportional hazards models, adjusted for age, sex, education, physical activity, smoking, body mass index, height, weight gain during follow-up, diabetes, family history of cancer, number of 24-hour dietary records, and baseline intakes of energy, alcohol, sodium, saturated fatty acids, fibre, sugar, fruit and vegetables, whole-grain foods, and dairy products

So I have a more interesting question here: how effective are these sorts of statistical methods? Is it plausible to start out with a highly-biased population [1], adjust for twenty or so distinct factors, and get results that are actually meaningful?

[1] As I understand it, the study population consists of 102k French adults, self-selected via finding the relevant website and their willingness to go fill out a bunch of surveys. As TFA notes "[...] 78.5% of the participants included in the analysis were women, which could be considered a selection bias. Additional biases noted by the researchers were that participants were more likely to have higher educational levels, and to demonstrate health-conscious behaviors."