On the whole, I prefer adventure hooks that appeal to the characters' motives, rather than being nailed onto their backgrounds. Curiosity is a powerful motive, as are duty, money, fame, and the desire to make the world a better place.
Yeah this is it. Backgrounds and motives are often deeply interwoven, of course, the Darkstryder campaign for SWD6 has a lot of pregen characters whose motives stem from their backgrounds, as an example.
But keying off the actual motive rather than simple background facts is important. If you have a character and their uncle was murdered, you have to know the personality and relationship to guage what the motivation would be. I've seen a few adventures, and also computer games where without establishing any emotional connection or real reasoning, they simply tell you you're "seeking vengeance" or whatever, and it just kind of falls flat.
This is obviously a particular issue with pre-written adventures but which don't have specific characters associated with them. If you have pre-gens, it usually solves that problem, so long as they're clearly written.
It doesn't do anything to rule out the premise of "There are goblins in a nearby cave"; or any other adventure along that line. The most probable explanation for that event is simply that there are a lot of caves full of goblins.
It also doesn't rule out most adventure premises that don't involve the PCs specifically. If someone's brother was kidnapped by ninjas, and the PCs are the only ones nearby who are capable of dealing with it, then that isn't particularly unlikely; while ninja kidnappings aren't exactly common, there are a lot of potential targets for them in the world, and the PCs are often the most capable people in any region they travel. If the ranger's brother is kidnapped by ninjas, then the most likely explanation is that the GM is messing with you.
That's a kind of weird meta-gaming approach that implies an actively anti-cooperative attitude towards the DM, and does in fact rule out a lot of adventure premises, particularly in non-D&D RPGs. But my main issue with it is that it's verging on the adversarial, as you're basically attempting to test every scenario, and if you feel like it is "unlikely", rejecting it as "the DM messing with you". If you, for example, had Buffy campaign that mirrored the plot of the actual Buffy TV show, you'd presumably reject about 1/3 to 1/2 the episodes/adventures as "the DM is messing with me".
Now, in real play that may well not be how you behave (indeed I doubt it is), but that's the behaviour you're outlining. Essentially rejecting events in the fantasy world because they fail to match up to what is necessarily a somewhat arbitrary and subjective to test of "is this contrived by the DM?". Two similar people could have the same thing happen and come out with completely different results for that. With your "brother kidnapped by ninjas" example, a lot of players will simply just go "Hot damn, I better rescue him!", but apparently you will go "Blast that DM and his cheap tawdry unimmersive storylines!" or something. Which highlights the subjectivity and arbitrary-ness of the test.
Well, yeah, up to a point, but also no. The players need to work to invest themselves and be active participants in the game. Passive players give me the pip. The GM provides openings and scenarios, but its up to the players to breath life into them.
Yup, though experience with quite a number of groups over the last few decades suggests that the game is also in the mix here. Some games make it incredibly easy for players do this and really encourage them to, others actively make it tricky. PtbA for example is incredibly reliable in getting players involved, in my experience, but D&D 5E can actually encourage passivity a bit. Obviously DMs can work to improve the situation, of course.
Adventures/APs can be the same way. I've seen ones which really pulled the players in by immediately giving them stuff to engage with, people to talk to, things to think about, and I've seen others, especially those obsessed with an aura of mystery, where the players almost slide off it like some sort of frictionless surface, because there's nothing to really engage with, just a sequence of events or rooms in a dungeon or whatever.
). Reactive players more or less passively wait for the DM to roll up the plot wagon and dole out the adventure du jure. 
