... More likely sick people are more likely to take vitamins than healthy people.
Also, people who know they are eating a crappy diet take a multi-vitamin.It does them no good, so they have worse health outcomes than people who eat a healthy diet and don't take a pill.
Actually, the epidemiologic literature consistently shows a positive relation between multivitamin use and health. The question is, does the multivitamin contribute to good health?. If it doesn't, then it must positively correlate with something that does. It could be that that people who know they are eating a crappy diet, and hence take a multivitamin, actually have less crappy diets than people who don't know that they are eating a crappy diet.
For example, people eating a diet high in processed grains and sugar, but low in fat and animal products might think they're eating a healthy diet, but they're not.
That goes double for most vegan diets.
It could also mean that multivitamin/supplement use correlates with an overall concern for health.