Rincon was killed because of articles he wrote about small-scale drug-dealing in the city of Villahermosa for the Tabasco Hoy newspaper, authorities said in a news release.
The kidnapping suspects who described the killing belonged to a cell from Los Zetas cartel led by Jose Akal Sosa, according to the state attorney general's office. Akal Sosa, who was arrested with the others in 2007, verified the accounts, the office said.
The suspects' information led to a search warrant of a property where police found charred remains of at least five people, metal drums and clothes in the trash, the news release said.
Several DNA tests to confirm the identities of the remains were unsuccessful.
According to the state attorney general's office, Rincon and others were beheaded and dismembered before being doused with diesel fuel and burned inside the metal drums.
The details of Rincon's death come at a time when Mexico's government is under pressure from international press freedom organizations to make progress in investigations of crimes against journalists.
Three journalists have been killed in Mexico this year.