Well physics says contrary. Velocity is a vector quantity. That is, it is directed. If we assume that the nuke is falling perpendicular to its original target and has a speed of Mach 20 then its velocity in y axsis is 0. Now to move the nuke around on its y axis you need to add thrust to it. Here is where you would say the base mounted side mounted thrusters will be used (which by the way are used RCS purposes). But this will have a side effect too. If the thrusters are fired only on one side (so as to give a Y component of thrust to re-target), the nose will flip the opposite side making the RV tumble, exposing the non sheilded areas and the harsh hypersonic atmosphere outside will, in scientific terms, shred the re-entry vehicle. The radioactive parts also won't survive the hypersonic fall in oxygen rich air.