UNC's response, which is signed by Kansas lawyer Richard Evrard, said the University has not been treated fairly and consistently.
"The University wants to move this matter forward, but now faces a third Notice of Allegations in a process that increasingly lacks clarity on what the University is expected to defend," the letter said.
Cunningham reiterated that point in a conference call after documents were released. He said UNC is concerned that NCAA staff members and the Committee on Infractions have inconsistently applied bylaws during the investigation.
"We believe that the process has gotten off track, and we have serious concerns about that," he said.
In UNC's case and in other cases, Cunningham said the NCAA has not followed its own rules. He said the University, in contrast, has followed correct processes and been transparent.
"We're held accountable to the standards, and when they violate the process, I don't know what our remedy or recourse is, but I'm certain we're gonna explore every one of them," he said.
Cunningham did not give a direct answer when asked if UNC would consider suing.
Like the two older NOAs — from May 2015 and April 2016 — the latest one alleges multiple Level 1 violations, which is the NCAA's most serious type of misconduct.
Unlike the first NOA, the third one does not name counselors in the Academic Support Program for Student-Athletes, but the program still plays a role in the allegations.
"Further, (the University) did not demonstrate control when it failed to provide adequate guidance, rules education and supervision to institutional representatives employed with (ASPSA)," the new NOA said. "These failures allowed the violations in Allegation No. 1 involving ASPSA to occur and to go unchecked for multiple years."