Lanefan
Victoria Rules
If the players have their characters take steps to seek those interesting things out e.g. listen for rumours, check with contacts or temples or guilds etc., then yes - ideally they'll find some.But that kind of thing can happen. I can certainly understand how if it happens all the time, it can put some folks off, but I would make two comments on that.
One, I don't think that the story now type games I play have a very high instance of this. It's not about things somehow in some unexpected way connecting back to the characters... it's about the characters actively seeking out the things they seek out. No one watches Kill Bill and wonders why the Bride is always running into the people who betrayed her, do they? Shes actively seeking them out!
Second, I think that whatever happens instead of the perceived contrived thing is just as likely to be contrived. So instead of arriving in town with a specific goal in mind, the party arrives with nothing in mind... but then things come up! Because of course they do. Hooks spring up all about... this NPC has a favor to request, and that NPC has lore about a nearby site, and another wants his brother rescued from the Brotherhood of the Ebon Hand. If we don't go to the nearby caves, eventually the goblins will attack the town!
No one's worried about the fact that strange things always happen when the PCs are around! That's all considered happenstance and isn't contrived at all!
My view is that the PCs are gonna do interesting things. There are going to be events happening no matter what.... that's the point of play.
But if they don't take such steps - particularly fairly early in the campaign - it's entirely possible they're just gonna sit around in the pub until we all get bored.

Later in a campaign it's much easier to draw on their own played history if I need to bootstrap things: "Remember that Baroness Caratina who got you lot out of a jam when you were here last summer after the Ogre Caves run? Well, her messenger is here asking for you, seems she'd like a favour from you in return..."