I think a lot of the worries about murders and rapists on trails are leaving out one factor: they are often crimes of opportunity in that the victim of choice was not selected carefully ahead of time and stalked, rather, they are "encountered" and decided on a whim. This makes determining the safety factor on a hiking trail much harder concerning the human element.

as for the nature and group factors, i would say that from personal experience, sometimes it's much better to hike alone as long as you prepare well.

The last long hike I did in a group, we split up some of the equipment so that we reduced weight from excessive redundancy. This would have worked well if everyone had the same pace. Needless to say, at the end of the day, it was a disaster because the "group" was split by pace and impatience and necessary items were not available because they were with the other "group" who were running ahead and never stopped to look back.