So I understood that the people giving out "random" quests, but I was amazed when both the Whiterun attendant and the Companions gave me the same quest (the text was actually different) to clear out one of the camps North of the city. In fact, I was was worried it was a bug, so I saved the game, backed up to a previous save, saved that up in a slot, and then sought off to defeat the leader of the camp, practically expecting a bug when the quest(s) were done.
To my surprise, it went swimmingly. Killed the bandit leader, went to both factions and got my rewards.
It seems a lot of these quests are to "kill the bandit leader", so I suppose I should have expected testers to run into this, but it was nice to see it work. My only concern now is that all the quests of this nature (random) are to "kill the local bandit leader" - I do hope they might vary a bit from time to time -