"Eating more vegetables was associated with a small but statistically significant reduction in cancer risk"

It's a 4% reduction for 2 extra servings of veg, which they helpfully illustrated by saying if you had 10% chance of cancer without vegetables, eating them would mean you would then have a 9.6% chance. I'm guessing that was an attempt to downplay the significance. If they'd said for every 25 people who get cancer, one wouldn't then it might have seemed more like good news.

They also claim that number could be wrong and list various factors why the results could be skewed, but never explain why they think the number would only get worse, rather than better due to these confounding factors.

Not dying from X or Y increases your risk of dying from Z!