One of the diseases of videogames is quest-givers who ask you, a total stranger, to solve their problem. Most people don't trust total strangers enough to even tell them what their problem is. The exceptions would be people who desperately need someone, anyone to solve their problem, and are presumably asking everyone. E.g. the postings for Witcher jobs: if you have a dragon problem, you don't care who kills your dragon, or who knows that you have one.
One of the nice things about quests in We Happy Few is that quite a few of the townsfolk do, in fact, know the player characters. So right away it makes more sense if they ask for help.
There's a simple fix, though. Instead of having the quest-giver offer the quest and then offer a reward, give the player character a reason to know that the quest-giver can give that reward. Then if the player character asks, the quest-giver can say, "Well, I might do that for you, but first you have to do something for me." To me that feels more natural.