Initial 'conflicting' reports from the popular walk near Settle suggested that 'multiple casualties' had fallen into the River Doe near the Snow Falls section of the 8km trail and possibly been swept away on August 18.
The Cave Rescue Organisation has now released full details of the incident after witnesses feared that there had been fatalities when they saw both of the Yorkshire Air Ambulance helicopters land at the scene.
Three people, all members of the same family, were involved in the incident and none entered the water. A 46-year-man slipped while carrying his six-year-old daughter, and they fell down the bank towards the river's edge. The man's partner, a nurse, slid down the bank to give first aid, and paramedics found all were conscious. No further casualties were found.
The father suffered a head injury and a fractured leg, and was taken to hospital by road ambulance. The mother and child had only minor cuts and bruises.
The Cave Rescue Organisation, which provides the mountain rescue response in the Craven area, is often called to incidents at the Ingleton Waterfalls Trail, a privately owned visitor attraction, and has previously issued safety advice warning walkers to wear correct footwear and to be aware of the terrain and their own capabilities.