It was never my intention to imply that anything ceased to exist when not in proximity to something else.
Impact on the world through storytelling works wonderfully in a storytelling style campaign. If the campaign is not being played in that style then the minion concept is meaningless. Thus if it is your assertion that certain interactions are best handled through the medium of the story then a story based campaign is the assumed mode of play based on rules that support this.
It is one approach, not all, to running a campaign.
There are some other ways of looking at it that may help this disconnect.
From designer description and examination of their presentation in the monster manuals (Ogres are a good example of this) minions seem to be primarily an administrative abstraction. Their purpose (much like the mob monster rules from 3.5) is to allow a large number of creatures in a fight while not massively increasing the administrative burden on the DM.
Consider then that the minions are simply being represented at a lower time resolution than other creatures - to a high level character a low level creature may take two hits to kill at 95% to hit and it may have a 10% to hit him to do an average of 15 points of damage. We could alternatively represent this creature as a higher level minion which is hit 50% of the time and hits 50% of the time for 3 points of damage. On average, it will take our character 2 attacks to kill the monster either way and they will take on average 3 points of damage doing so. Do you get some odd edge cases? Sure, but you always will do as assuming any system is the physics of the game world.
Is it a pretty big abstraction? Sure. IMO though, its of the same order of abstraction as turn based combat or even the existance of hit points.