Most of the vegetarians/vegans I know have a pretty shitty diet - lots of highly processed grains (bread, pasta, and other fillers), sweets, desserts, sugary drinks (and other "regular" products with added sugars), and otherwise not too diverse of a diet.
Don't know if that's a representative sample of vegetarian/vegan population, but it's not unlikely the case. Hence, the link between the veg* diet and cancer is not hard to imagine.
The main issue with (a lot of) these research papers, other than having bad data to begin with, is the lack of control for other parameters: what exactly do those surveyed meat-eaters and vegetarians eat, and what their lifestyle choices are (e.g., vegetarians are generally more health-conscious, so they often exercise, don't smoke/drink as much, etc.).