I see a couple of ways to think about it:
If JR is innocent: He just wants some peace and quiet, his daughter was murdered, his wife has passed away recently, the past 10 years have been a literal media HELL for him and his family, on top of the agony of losing a child in such a horrific manner..etc...
If JR is guilty: well, all sorts of things spring to mind...if he knows the guy and is afraid Karr will implicate him, or maybe he thinks that renewed interest will shed some new light on the case possibly exposing his guilt.