In years past, USAAC/USAAF/USAF target ranges often had large bullseyes that often had a small hut at the center.  Thus arose the slang for hitting dead-center as having "shacked the target" and in general for using the slang "shack" to mean the same as "on the nose," "exactly," or "on target."

 

I suggest that you should not be quite so hasty with some assumptions in your first paragraph--although I am not suggesting they painted huge bullseyes a mile in diameter, either.  Also, the accuracy of a missile can be estimated as a collection of error budgets related to the critical timing of each stage shutdown and the next stage ignition, and ability to make velocity (not just speed) corrections in flight, the accuracy of the position data for the target, the launcher, and the missile, etc.--which assessments may be fed by all the typical range of sources of intel.