Mr. Biancardi wrote about how the court had ruled against him. That drew attention from others who asked for articles about themselves to be taken down.

One of those demands was from Vittorio Pecoraro, now in his 80s, who was stabbed by his brother , Umberto, in the 2008 seaside restaurant brawl. The brothers were arrested after the fight. Assault-related charges against Vittorio Pecoraro were effectively dropped when the authorities did not pursue them.

Vittorio Pecoraro sued Mr. Biancardi, citing the right to be forgotten. Mr. Biancardi refused to remove the article. The story had been based on information from the police, he said. Nothing was factually wrong.

But Vittorio Pecoraro argued that his privacy had been violated. The article was easily available and searchable online, and he had not been convicted of a crime. Yet because of PrimaDaNoi, what he considered a humiliating family argument had become the first thing that many people knew about him and his pizza and seafood restaurant, he said.

“I have a reputation, I have been here for 50 years, I am known all over,” Mr. Pecoraro said in an interview at the restaurant, Positano, where the 2008 fight had occurred.

His lawyer, Paolo Sardini, said Google was not targeted because the article was Mr. Biancardi’s responsibility.

Umberto Pecoraro’s son, Vincenzo, said his father declined to comment.

In 2013, an Italian judge ruled in favor of Vittorio Pecoraro and ordered PrimaDaNoi to delete its stabbing story, saying the information in it was old and no longer in the public interest. (Mr. Pecoraro didn’t ask for another PrimaDaNoi article about the incident to be deleted because it didn’t rank high in Google’s search results for his restaurant.)