That is not necessarily a flaw in their claim; a similar speed differential is an issue for atmospheric interception of the warheads from an ICBM. The trick to intercepting something at Mach 15-30 (although news reports suggest this rock might have been traveling at Mach 80) with something at Mach 5 is to launch from near its path and in front of its position, and that could realistically have been done. I don't believe the claim either, but not because of the relative speeds of the rock and the missile. I just assume that communist politicians lie.
I don’t believe these claims, but not because of lying politicians but because of physics. Not only do you have a big difference in speed between the rock and the missile, but a bigger difference in momentum. The rock is much, much larger and more massive so if the missile were to be launched at EXACTLY the right time then yes, it could realistically be done but it would have no effect because the rock would smash the missile to pieces and continue on its way. The only way to destroy such a rock with a much slower missile would be if the missile was carrying a powerful enough contact burst nuclear warhead. I’d say the warhead would need a yield of at least 500 kilotons. Nevertheless, we would need much faster nuclear missiles to realistically intercept and destroy meteors. Which BOTH countries should develop.