For years, AdvoCare recruited hundreds of thousands of consumers across the country to market its health products, promising “the average person a financial solution that will enable them to earn unlimited income,” the F.T.C. wrote in a complaint filed in federal court in Texas on Wednesday.

In reality, the agency said, AdvoCare pushed participants to recruit distributors rather than sell products, instructing them to make exaggerated claims about how much money people could make through commissions. In 2016, 72 percent of the company’s distributors did not earn any compensation, while an additional 18 percent earned between 1 cent and $250, the complaint said.

“Legitimate businesses make money selling products and services, not by recruiting,” said Andrew Smith, director of the F.T.C.’s Bureau of Consumer Protection, in a statement. “The drive to recruit, especially when coupled with deceptive and inflated income claims, is the hallmark of an illegal pyramid.”

In a statement, AdvoCare denied that it operated as a pyramid. “We strongly disagree with the F.T.C. allegations, but we are committed to abiding by this agreement and moving forward,” said Patrick Wright, the company’s chief executive.

Mr. Bush was a keynote speaker at AdvoCare’s sales and training conference in Frisco, Tex., in 2018, and Mr. Brees has served as the company’s national spokesman since 2010. Representatives for Mr. Bush and for Mr. Brees’s National Football League team, the New Orleans Saints, did not respond to messages seeking comment. AdvoCare said that Mr. Bush had been hired to appear at the conference through a speaker’s bureau and that he had no relationship with the company.