Kind of a crude irony. As for years (It's entire existence, I think) WJ(K)W simply didn't show "The CBS Late Movie/CBS Late Night" programming by choice. At one point, I think it was even deferred to WCLQ. My thinking is WJW anticipated Letterman before the network switch was announced, and brought on Arsenio believing they'd have an all new programming block and audience for late night.
WJW (as Fox) wasn't completely innocent of passing up network shows. I think the "Fox Kids" and "Fox Kids Club" were picked up by WBNX. To this day the 11 A.M. "Fox NFL Kickoff" show is sent over to Channel 8.2