The N.C.A.A. has a consistent policy of not commenting on investigations, and the tense back and forth between Roe Lach and Chizik offered rare insight into one of the most contentious cases in recent N.C.A.A. history.

Both the N.C.A.A. and Auburn acknowledged last year that Newton’s father, Cecil, had offered his son’s services to Mississippi State for $180,000. Cam Newton told the N.C.A.A. that he had no knowledge of the proposed transaction. Soon after, in a controversial decision, the N.C.A.A. declared him eligible to play the rest of the season. He went on to lead Auburn to the national title and win the Heisman Trophy. He now awaits his new role as quarterback for the Carolina Panthers.

Auburn, the N.C.A.A. and the SEC declined comment on the exchange at the SEC gathering.

While Chizik has repeatedly said that he and Auburn did not break any rules in recruiting Newton, Roe Lach made it clear that the N.C.A.A. is not done investigating.

“Obviously, I think that she was serious, and I obviously thought it was a good message, because you could tell that she and they are serious about what they’re doing and trying to do what they have to do to clean up some of the bad elements in college athletics,” said Vanderbilt Coach Kevin Stallings, one of four SEC basketball coaches who confirmed the exchange.