He also said the NCAA investigation into the matter may be nearing an end.
University of North Carolina Chancellor Holden Thorp also attended the meeting. The board is the policy-making body for the universities within the UNC system.
"Because there has obviously been a story unfolding at UNC Chapel Hill since our last meeting, it seemed appropriate that the chancellor be prepared to answer questions," said UNC Board of Governor's Chairman Hannah Gage.
News of the investigation became public in July. The NCAA began investigating claims that some players were involved in inappropriate contact with sports agents, which is a violation of NCAA policy. And last month, new claims about a tutor writing papers for players surfaced.
On September 4, the day before UNC's season opener against LSU, UNC announced six players were ineligible to play and six others were not allowed to play while the investigation continues. UNC said the students held back violated university and/or NCAA rules but did not give specifics.
Then on September 6, assistant coach John Blake resigned. Recent phone records raise questions about his ties to an agent that may have had contact with some UNC players.
The phone records in question suggest a possible lead into the investigation of whether players may have taken gifts from sports agents. North Carolina Secretary of State Elaine Marshall is investigating that claim.
Thorpe said at Thursday's meeting that the investigation in moving forward quickly.
"As of right now, we feel like we have all or most of the facts that we need to decide with the NCAA who will be eligible. And we're in the process of documenting all of that and working through that process now," he explained.
Board members repeatedly asked when will final answers come. Baddour suggested soon, but offered no firm time table.
"I don't want to create expectations that can't be met. And I think it's important that we realize each case is different," he said.
Questions ended when UNC President Erskine Bowles stood with Chancellor Thorp and Baddour at the podium.
Bowles said he absolutely trusted the academic probe at Chapel Hill, and board members sounded pleased.
"I am honored to have their support and do everything I can to maintain that trust and confidence," said Baddour.
One member of the board asked how far back could the allegations of academic fraud actually go. Baddour said "prior years." And the chancellor said the probe is taking longer because some players have been at UNC "for a while."