About to go read the study, but my guesses are;
- Probably using a food diary or similar recall based method to figure out food frequency
- Likely not controlling for whether people are health focussed or not
- The cancer link will be measured by risk of death by cancer, obfuscating whether the individual seeks treatment
- The plant heavy nature will be vague, grouping all plants together rather than any specificity, eg sugar beets and kale both count the same
Back shortly to update.