You are correct regarding the physics, Mark, but I can still see this being used as a political/psychological weapon. The public and politicians are at least aware of the threat posed by NEOs, but not what it would take to move and aim them.

All you need is some group saying they have control of a space rock and are going to drop it on NYC unless their demands are met and most people won't start whipping out their slide rules to judge the true danger level of the threat. They will panic and act like scared sheep.
The similarly uneducated media will just feed into the panic.

That may be all that is needed to achieve the enemy group's desires.