The bikes were on the trail and the purse was on the lake side of the fence, 20 feet east of the bikes. It seems to me that the best explanation is that the girls went over the chainlink fence where their bikes were parked and Elizabeth lost her purse walking east.
If the girls were abducted on the path where their bikes were found, I think the perp would want to get them off the path as fast as possible, and that means straight over the fence, whether the girls wanted to go over the fence or not.
How about more than one perp handing the kids up and over? Or if there is a hole in the fence