It is possible that the instructor trained in one of the recognized organizations (aikikai, etc), but due to internal politics decided to leave the organization.
I think Frank nailed it.
Aikido history is replete with schisms in organizations, instructors coming up, then a difference of opinion about such-&-such comes up which can't get reconciled, and someone goes their own way.
Is the "new" school/dojo less? Who knows, we'd need to stick our noses physically in and see if they've got some true ability to decide that on a case-by-case basis, I think. Is the new school "official," though? To themselves, I'd say certainly. They can control their own official-ness, if they decide to not associate with any larger association. The problem with that is that unless you've got some magical-ninja talent at advertising (I'm assuming that you're trying to run the thing at least so it doesn't bankrupt yu personally), you may well need to be associated with someone, something, some association or governing body which will lend you their authority (real or perceived). I did this myself when I opened up Wasabi. True to historical form, the main organization I/we were in was the Fugakukai under Sensei Karl Geis (now deceased). But, that organization was going through... drama, which some (most? All?) reported was caused at the very top, though examples varied. In the end, in spite of a martial arts genius behind all the higher-level instruction, the organization fractured. Actually, it sort of collapsed, splintering into its many regional portions.
This was all going on while I was coming up through kyu grades and into the lower dan grades. At one point, I was learning my Tomiki-ryu from a single-person "organization, in Ray Williams over in Clear Lake. To my nosey point above, the instruction was top-notch, at least I thought so. I was learning cool stuff, and it was working the way it was supposed to the rare times I wanted/needed to do something, so i was content.
Ray ended up tying up with some similarly-ranked coleagues and forming a nascent organization they called the American Tomiki Aikido Association, which sounds way more formal and organized than we/they were. I wrote up the organization documents for that thing, by the way. It still exists, too. Let me check... hold please.
Sure thing, here's the FB group page...
American Tomiki Aikido Association
AND once again, organization drama reared its head.... and this one nearly died due to dojo-level drama here in Houston. My buddy & I got caught n the backlash, as we were head down on the grindstone working our way through the sandan testing/demo material. It sucked, being accused of "disloyalty," etc etc. It should have been aired on weekday afternoons between 1 pm and 3 pm there was so much soap in the drama.
Anyway, scroll forward to 2010 and Wasabi opens up. I had an upline of instructors I could reference, like Ray, but no organization to get cred from, so I ended up asking Ray's advice and he suggested that I get in contact with Nick Lowry (now retired) in OKC, at Windsong Dojo. Nich was putting together his own Windsong Martial Society, loosely associating the fractured school who wanted to have the fellowship, group capabilities, and credibility of a larger association. That's what I did. In the WSMS each school is independent, but you can go to other schools and visit, train for a bit, send students to other schools to test (thus getting some feedback on teaching criteria and standards) and so forth. That's been working well.
So, Wasabi was/is independent... but not. There ya go.