Not even just consumption, the healthy user bias also effects lifestyle factors. People who try to avoid artificial sweeteners because they think they are unhealthy likely make many other decisions to promote their own health (increased exercise, avoiding other carcinogens). The study attempts to control for some of these factors (exercise, smoking), but given the HR is only 1.15, I have trouble believing the correlation here is anything but spurious.
How can you tell that it was the artificial sweetener that led to cancer? And not one of the other hundred things people consumed during the day?