The other anti-supplement claim made is about folic acid and colo-rectal cancer. it is a well known fact that floats protect cells from becoming cancerous. However, if a person has pre-cancerous cells in the gut, often found in those with colorectal polyps, supplementing large amounts of folic acid can make those pre-cancerous cells grow faster, thus increase colorectal cancer risk. That is why I am not in favour of fortifying all food with folic acid, and caution against supplementing large amounts, e.g. 800mcg, unless you have good reason to, such as a high homocysteine level.
The guy referred to as making these claims at the recent American Association for Cancer research meeting, which is of course largely funded by big pharma, has not one paper published that I could find, and there are no details of any of new research as such, so I must assume it is just regurgitating old myths.
Have a look at https://www.patrickholford.com/advice/the-truth-about-antioxidants-supplements? for dissection of the antioxidant myths.