The Chicago Bears were one of several teams that interviewed Detroit Lions defensive coordinator Teryl Austin in recent weeks. Since that was for a head coaching job, the Lions had to grant the Bears (and other teams) permission to speak with Austin.
It turns out that the Bears also expressed interest in speaking with Jim Bob Cooter, who is the Lions' quarterbacks coach. Cooter joined the Lions last year after spending a season with John Fox in Denver, and Fox apparently had interest in hiring Cooter as his offensive coordinator in Chicago. That would have been a promotion for Cooter, but the Lions reportedly denied Chicago's interview request.
In the NFL's eyes, a promotion from position coach to coordinator isn't enough to force teams to accept interview requests. That's why the Lions had the ability to deny Chicago's request, and they took full advantage of that rule in order to make sure that they didn't lose their quarterbacks coach to a division rival.