The purse is interesting and could be the clue that leads police to believe that the scene could have been staged. Given that the bikes were on the trail side of the fence, next to a gate, and the purse was set down on the lakeside of the fence, it kind of looks like the girls simply parked their bikes, went through the gate, set down their purse and vanished into the water. The problem is that there were no shoes and no one would swim in a leech infested lake. It's like we have a suggestion (bikes, purse) that the girls went into the water, but the suggestion is incomplete.
The purse is set down near some rocks on a narrow shore with some debris (cardboard or board, logs, new plant growth) that is approximately 100 feet away from a forested area, but it does seem completely out of place. In my estimation, it would take about 1 minute to walk that distance and be out of sight in the trees.
I'm doubtful that the girls rode their bikes down the trail from the east side to the gate. Too many people have said that it is very creepy. I don't believe that someone walked between the double fenced area with two bikes and a purse. I do believe that Maiden Lane was where a vehicle was parked to take the girls away from the area. Is it possible that nothing matches up because one clue is wrong ... like ... staging rather than crime scene, cyclist tip, timeline, route ...