"I didn't realise I'd equalled the record. I go out to score goals, but I don't go out thinking about records," the Fiorentina striker said. "I'm playing for the team. If I've got four goals it's because the team are playing well," Batistuta said at Argentina's World Cup camp outside St Etienne. "I didn't come here to be the top scorer or the best player of the tournament. I came here to win the World Cup with Argentina."
Batistuta, who also scored four goals in the 1994 finals, is the joint leading marksman after two matches, having scored in Argentina's 1-0 victory over Japan before his hat-trick against the Jamaicans, when Ariel Ortega scored the first two.
Batistuta was the second Argentinian to score a World Cup hat-trick on his debut, when he hit three goals against Greece in the 4-0 win in Boston four years ago, after Stabile's treble against Mexico in a 6-3 victory in 1930, but has said that he was not out to prove anything to his national coach, Daniel Passarella.
Batistuta has played his way back into Passarella's team after being overlooked for a year. "I didn't come here for revenge. I was out of the team for a year, but I never thought that I needed revenge. I'm happy that I'm in form and well here," said Batistuta, the fourth man to hit two World Cup hat-tricks and the first in successive finals.
Although he is Argentina's all-time record scorer with 47 goals in 63 internationals, Batistuta will never beat one record - Stabile's average of goals per game. Stabile played only four times for Argentina, all during the 1930 tournament, scoring eight goals.
The other player topping the scoring list at France 98, Italy's Christian Vieri, believes goalmouth action speaks louder than words. Two weeks into the World Cup, the Atletico Madrid forward also has four goals and has found the net in all three of the matches that Italy have played.
He has eclipsed Roberto Baggio and Alessandro Del Piero to become the most talked-about forward in the Italian camp, but Vieri himself is saying little. "How many goals do you promise to score in the next round?" one reporter asked after Vieri's powerful header had set Italy on their way to a 2-1 defeat of Austria on Tuesday. "None. I don't make promises," Vieri replied.
"Did you ever dream you'd start the World Cup like this?" ventured another. "I don't dream," responded Vieri before moving on.
So long as Vieri continues to prosper at the World Cup, Italians will not care that the man they have christened "the ice giant" keeps himself to himself.
"He's kept something with him from his long sojourn in Australia - a distrust of conversation." noted the Gazzetta dello Sport newspaper this week. "He sticks to the bare essentials, just like he does on the pitch."
The brusque Vieri cuts an odd figure at Italy's training camp where most of his team-mates, in good Italian tradition, never tire of their own voices and are willing to chat with reporters from morning to night.
Perhaps his experience last season, when he was dropped by the Atletico coach, Radomir Antic, and fined for criticising tactics, has made him wary of speaking his mind.
One of only two foreign-based players in Cesare Maldini's squad, Vieri is one something of a nomad. Born to a French mother and an Italian father - also a professional footballer - Vieri was brought up in Australia and did not move to Italy until the mid-1980s.