Well, a back-spinning store hitting the water has a contact speed between the two that is much higher than the simple forward speed of the mine - it's that plus the perimeter spinning speed.
You are correct - the aerodynamic lift mentioned in the programme is fairly insignificant compared to the effect of the backspin.
The backspin gives the bomb a considerable rotational energy - when the bomb hits the water, part of this rotational energy is converted to kinetic energy in the upward bounce. This explains why on some of the videos the bombs were bouncing substantially higher than the aircraft that had dropped them.
The other part of the programme that they rather glossed over was the final drop with the "live" bomb. They implied that the explosives were contained in the bomb - but I very much doubt they were!