Quote: "The missile would have been semi-vaporised."
Not true. The missile fore-body immediately behind the seeker and guidance electronics, contains the fragmentation warhead.
Detonation will still leave a large part of the rocket motor and control fins intact which can then fly uncontrolled with residual fuel burn. Even if the motor is punctured in the explosion, it will cause the structure to tumble uncontrollably but unlikely to break it up completely. Don't forget, this is a SAM system capable of high-g manoeuvres (typically 30 - 50g) of monocoque construction and so of very high strength.
Given the initial kinetic energy of the missile at detonation (typical velocity 800 - 1000 m/s at altitude), large parts of the missile will travel some considerable distance in semi-ballistic trajectory away from the detonation point.
These parts will reach the ground perhaps tens of kilometres from the main crash area and therefore makes the missile parts recovery area huge.