Two lawyers for Mr. Jones, emailed on Tuesday, were not available for comment.

One of the InfoWars stories that is the subject of Chobani’s lawsuit involved a 2016 sexual assault in Twin Falls that drew national headlines. The InfoWars video promoted on Twitter on April 11 reported that three children involved in the assault were refugees, and then it gave details of Chobani’s policy of hiring refugees in the city.

The Twin Falls County prosecutor, Grant Loebs, said in an interview on Tuesday that the assault case had nothing to do with Chobani. He said he was not authorized to speak about the details because the case involved minors, although he noted that the local news media had been reporting on it since it happened last year.

Mr. Loebs said that on June 2, 2016, a 5-year-old girl at an apartment complex in Twin Falls was sexually assaulted by three boys, ages 7, 10 and 14. Two of them were refugees from Eritrea, and one was from Iraq. The children pleaded guilty to separate charges including sexual exploitation of a child and misdemeanor battery.

“There was no gang rape, no knife attack, and we did not charge anybody with rape because no rape occurred,” Mr. Loebs said.

The lawsuit filed by Chobani said Mr. Jones and his companies had declined to remove the reports or publish a retraction despite multiple written demands.

It said the defendants acted with “actual malice” to harm Chobani’s reputation and to discourage customers from purchasing its products. The lawsuit is seeking a jury trial, and the amount of “substantial damages” Chobani has suffered will be provided at a trial.

The lawsuit also noted that Mr. Jones was “no stranger to spurious statements.” It cited his previous contentions that the Sept. 11 attacks were orchestrated by the United States government and that the 2012 shooting at Sandy Hook Elementary School in Newtown, Conn., was a hoax concocted by those hostile to the Second Amendment.