What do you think about schools that aren't affiliated with any larger organization?
Define "unaffiliated."
There's some "schools" that just Joe Sensei in his backyard, teaching what he was taught 20 years ago when he got his first black belt. He's not been in touch with his teacher or done any continuing training in what he's teaching in most of that time. It may or may not be good -- but it's not necessarily what's being taught now. I've personally found that I sometimes need my teacher's eyes on me to figure out something that's drifted off... But maybe that's just me. And I know that my system has changed over the 20 years I've been training.
Then there are "unaffiliated" schools because someone isn't big enough to afford the club fees to their association, or some similiar reason, but they are active members who regularly get new/refresher/further training from their seniors in the system. Rank may not be "official" but it's credible, if that's what you're after.
And there are schools that just don't have larger organizations to link with, too. Some of these are the guy who bounces around for a few years, collecting techniques and bits of 8 or 9 different styles and starts teaching his own thing (whether or not it's any good is a whole different question!). Or they might be doing kickboxing or mixed martial arts (as examples) and don't really have a larger organization. Others are what I'll call legitimate masters/grandmasters of a system that just doesn't have a larger organization. They're it... at least for now. And sometimes the larger organization just folded or splintered with the death of a founder and the school is staying faithful to what the instructor was taught. Which has kind of led me in a circle...
The bottom line? Assess the teaching. Here in the US, black belts are becoming a dime a dozen... I've seen places go from being run by "masters" to "grandmasters" to "supreme ultimate grandmasters." Some are good martial artists, and others are... Well, I won't say, but I suspect most who get this far know! If the teaching and students are what you're looking for, decide if you need your training blessed by some higher organization. If you do -- you'll need a school attached to one. If you don't -- you've got your answer!