I mean potato chips are vegan. French fries are vegan, etc.
The key is whole foods. Unprocessed foods.
[0] https://www.cancercouncil.com.au/blog/the-sick-quitter-effec...
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.).
In my observations (I'm in the US) this statement is true of the majority of the population, including omnivores. 2/3 of the US didn't become overweight (1/3 obese) by being mindful of their diets.
There are a lot of vegetarians in India on traditional diets that don't include highly processed foods with added sugar. I think it's safe to say that most Indians eat vegetarian food most of the time. Meat is just something most people in India can't afford everyday.
For me it was for standard 'moral' reasons and so eating junk food is still acceptable.
Eventually I picked up the health reasons angle (and discarded all the junk food) and moving to mostly a plant based diet (mostly vegan).
Now that may be because of your top point, most of the meat consumed in the US is processed in some way. I think the biggest culprit of meat-related cancer (?) is preserved meats.
I don't know. I just wanted to admit to being a little shocked at the whole vegetarian/cancer link. You often hear the opposite of that.