Heck, to me, it could be something between the two. I mean, what je ne sais quoi made the folk hero into a folk hero in the first place? Probably some combination of charisma, looks, cleverness, and personality (none of which has to be reflected in ability scores, though it would be easier to understand if they were - people are a lot more complicated than can be reflected in six numerical scores after all) that makes common people just plain drawn to them.
It doesn't have to be magical, or fate-driven, or anything like that. This kind of stuff happens in real life. I don't personally think that it's that much of a stretch that a "folk hero" character could quickly make a commoner friend in a new village full of people that someone would offer her a place to stay. It's not like the entire village needs to trip over each other trying to be the first to make the offer!
I DO think that it would be better if the Background Features were written with two or three examples of the kind of things that a PC can expect NPCs to do for them (this is why I describe them as "limiting") so that a DM has more guidance to work something in that satisfies them, but I can see how that approach would not only take up more space, but require even more "DM fiat", which is often seen as "bad".