The person spoke on condition of anonymity because no statements were authorized.
Major League Baseball started its rebuttal, and it was possible the hearing would conclude Friday, the person said.
After the hearing finishes, the sides will set a schedule for briefs. The matter then will be turned over to arbitrator Fredric Horowitz for a decision.
The New York Yankees star walked out in the middle of the 11th session Wednesday, furious Horowitz refused to order baseball commissioner Bud Selig to testify. The move, followed by angry statements accusing Selig of bias and the entire arbitration process of flaws, appeared to be a prelude to a lawsuit challenging whatever ruling Horowitz makes.
Outside MLB's offices Thursday, representatives of the New York Hispanic Clergy Organization, including state Sen. Ruben Diaz, held a prayer vigil to express opposition to Rodriguez's discipline, which was assessed by MLB for alleged violations of the sport's drug agreement and labor contract.
Rodriguez was suspended by MLB on Aug. 5, and the three-time AL MVP was allowed to keep playing pending a decision on the grievance filed by the players' association.
"I lost my mind. I banged a table and kicked a briefcase and slammed out of the room," Rodriguez said Wednesday during a 40-minute interview on WFAN radio. "I probably overreacted, but it came from the heart."
MLB argued that it could decide what witnesses it wanted to present to justify the discipline, since the penalty must meet a "just cause" standard. MLB said chief operating officer Rob Manfred spoke to reasoning behind the discipline during his six hours of testimony.
Rodriguez and the union asked Horowitz to compel Selig to testify.
"In the entire history of the Joint Drug Agreement, the commissioner has not testified in a single case," the commissioner's office said in a statement. "Major League Baseball has the burden of proof in this matter. MLB selected Rob Manfred as its witness to explain the penalty imposed in this case. Mr. Rodriguez and the players' Association have no right to dictate how baseball's case is to proceed any more than baseball has the right to dictate how their case proceeds."
Rodriguez lawyer James McCarroll issued a statement Thursday pointing out that this case is the first grievance under the drug agreement involving discipline that didn't stem from a positive test and involved "the commissioner's discretion and decision-making." While he said the commissioner in the past "was harshly criticized in the arbitrator's decision for not voluntarily appearing at a grievance," that statement appears to refer to arbitrator George Nicolau's 1987 decision cutting Peter Ueberroth's suspension of pitcher LaMarr Hoyt from one season to 60 days.
Horowitz, chosen by management and the union as their independent arbitrator last year, has the discretion to eliminate the suspension or alter it. The statements by Rodriguez and McCarroll made it appear the 14-time All-Star intends to sue MLB and the union unless the penalty is eliminated.
Rodriguez already has filed one suit against MLB and Selig, accusing them of a "witch hunt," and another against the Yankees team physician and his hospital, alleging malpractice in the diagnosis and treatment of a hip injury.
Manfred is technically part of a three-person arbitration panel that also includes union general counsel David Prouty and is chaired by Horowitz
"I'm done. I don't have a chance," Rodriguez said during the WFAN interview.
McCarroll blamed Horowitz for precluding evidence Rodriguez wanted to introduce and hinted of a court fight.
"Whether the case is finally decided in this forum, created by Major League Baseball, Bud Selig's forum, or another forum, nobody is throwing the case out," he said.
Rodriguez denied using performance-enhancing drugs or obstructing MLB's investigation into the Biogenesis of America anti-aging clinic. Rodriguez was the only one of the 14 players disciplined this summer to challenge his suspension.
Rodriguez said four years ago he used PEDs while with the Texas Rangers from 2001-03. He has denied using them since.
"Over time, the arbitration process in baseball has been amazingly pro player," MLB spokesman Pat Courtney said. "It was that process which created free agency. It allowed Steve Howe to remain on the field despite numerous drug violations and resulted in the shortening of suspensions like John Rocker's. The notion that this same process is not fair enough or good enough for Alex Rodriguez is ridiculous."
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