It does seem silly to intercept. The computers could ascertain that the trajectory was unlikely to have originated on Earth in milliseconds.
Modern terminal guidance systems are all imaging based. Or at least the US ones have been for a couple decades; I imagine the Russians are using something at least vaguely similar.
Basically, the missiles latch onto the target visually and are capable of recognizing their target from the details of its appearance (in an air defense context, not just "an airplane" but "that specific airplane"). It is why, contra Hollywood, modern terminal guidance systems are nigh impossible to spoof. The missile knows what the airplane looks like and can read the tail number off your craft, so as long as it can locate it (even if it temporarily loses sight), it is likely to hit unless the motor runs out of gas. Heat has little to do with it, though the imagers often work in broad spectrum infrared.
Lots of smaller, impacters with kiloton-class impact energies are never discovered or discovered at the very last minute. This looks like a pretty small rock in terms of damage done so it could easily have been missed by sky surveys.