But they don't necessarily say what those confounding factors are in the abstract (I'm assuming they do in the full paper but I don't have access).

It's easy for me to imagine tons of confounding factors that are associated with vitamin supplementation, e.g. wealth (wealth is associated with better health outcomes nearly everywhere you look), diet in general, exercise levels, etc. I highly doubt they accounted for all of these.

Then the confidence levels would blow up.