I have a different reading of all this. I don't think PR in a case like this is any indication of innocence. His innocence has already been called into question, and that's why he has defense attorneys. Voyles is known for his work in high profile cases -- this *is* what they are paying him for.
Staying off the radar is only a good move if it's an option. JR already tried that, but hasn't been able to escape the public backlash. While his lawyers can (and likely have) shut down blogs that call him out for not cooperating with the investigation, having a victims parents publicly do the same, and accuse you of lying, is far more damaging. This is not just about reputation. Negative publicity can affect things like plea bargains and whether or not a case ever goes to court. So in cases with a lot of media attention, PR can be a key part of defense strategy.
Finally, if JR is guilty, what exactly is the risk of him meeting with LS's parents? It seems they may already question his innocence, so that's not it. He has his defense attorneys present, and they would not allow him to reveal information that would implicate him. This is their job, whether or not that information exists.
On the other hand, the benefits seem pretty clear. The fact that it was JR's defense lawyers who notified the media is a good indication that this meeting was in JR's interest. We don't know what (if anything) he shared with the Spierers, all we know is what his lawyers chose to share with the media. And that is a glowing report of JR's cooperation with the investigation. For those of us following this case, there is nothing else new about the extent of his participation in this press release, they just make it sound a whole lot better and use textbook strategies (like reframing "no comment" to "we are not allowed to disclose any more information") to imply further cooperation.
And apparently, this seems to have worked, given the reactions.
Anyway, my intention here isn't to insist that JR is guilty but to give my opinion that the overall goal of this kind of 'cooperation' appears to be managing the media and JR's defense, and as a result, only tells me that his lawyers are doing their job.