What is the meaning of this statement "If any diode has fully recovered before the V across it starts to swing, there is no reverse recovery current"?
The charge storage of a junction diode is a bit like having a tiny battery in parallel with it. During forward conduction, it 'charges up'.

If the voltage swings abruptly negative, then that charge must flow out again through the terminals. This is the reverse recovery current. 

'Fast' diodes are engineered to have less charge storage, and/or faster loss of the charge when the diode is no longer in forward conduction. Once the voltage has dropped to zero, this charge storage 'battery' starts running down. Charges diffuse within the junction, and doping with certain materials, gold for instance, can increase the rate at which charges recombine. If the voltage hangs around near zero for long enough for all the charge to have dissipated this way, then when the voltage eventually goes negative, there's no charge left in the junction to drive a reverse recovery current.