Inside a South Carolina factory, in industrial vats that stand five stories high, batches of algae are carefully tended, kept warm and fed corn syrup. There the algae, known as Schizochytrium, multiply quickly. The payoff, which comes after processing, is a substance that resembles corn oil. It tastes faintly fishy.

Marketed as a nutritional enhancement, the oil is added to millions of cartons of organic milk from Horizon, one of the nation’s largest organic brands. Rich in Omega-3 fatty acids, the oil allows Horizon to advertise health benefits and charge a higher price.

“DHA Omega-3 Supports Brain Health,” according to the Horizon cartons sold in supermarkets around the United States.

What the Horizon milk carton doesn’t advertise is that some of its contents were brewed in closed stainless steel vats of Schizochytrium. This omission avoids any ick reaction from shoppers, but consumer advocates say it also dodges a  key question: Is milk supplemented with an oil brewed in a factory really “organic”?

“We do not think that [the oil] belongs in organic foods,” said Charlotte Vallaeys, a senior policy analyst, at Consumer Reports. “When an organic milk carton says it has higher levels of beneficial nutrients, like omega-3 fats, consumers want that to be the result of good farming practices … not from additives made in a factory.”