In the past, these rejected lots were almost exclusively what was released as surplus.  The military doesn't surplus good, in-spec ammo unless the caliber is obsolete, so back before 97, when surplussing ammo was legal, what was released was all of the junk ammo.  And this ammo is now what's being demil'ed by Talon and reassembled (hopefully they're not using bad brass or bullets!).  As end users, we're almost never told what the original problem with the ammo was.  I'm not even sure the military released this information at the auctions where it was sold to distributers.

Now, small amounts of military ammo still sometimes make it out to the civilian world, usually via police resales.  The military sells and often gives police departments ammo.  In some cases, the department will have standardized on different ammo, and chooses to sell the ammo to their distributer for trade/credit towards the ammo they prefer.  The distributer will then sell the military ammo somewhere (often at gunshows) at a nice profit.  This ammo is normally the top-shelf stuff.