Gray - I love your home-spun, back porch analogy (you must have had an interesting childhood if those are memories you are drawing on for inspiration.) but you miss the obvious.
Yes, the stretcher spins slowly at first because the downwash is limited at a distance below the helicopter.
If you have understood what happened on the video, you will realise that the closer the stretcher gets to the helicopter, the stronger the downwash effect and the larger the torque force applied to the cable - it is not a constant, small force that can be easily overcome with a friction device.