If an instructor's budo "lineage" can not be traced back to Morihei Ueshiba, should what s/he is teaching be called "aikido"?
(Chuck here, posting in MLE's name 'cause I still can't get her logged out and me logged in at home. Of course, Emily says the reason I can't do that is because SHE'S the aikido person and I'm one of those koryu-lovin' darkside evil budo bunnies. She also mumbled something about the page code tapping into our ki, leaving cookies and checking browser compatibility ...)
Jun, you're a funny, funny boy. I love that about ya.
You left out the best answer: 'It depends.'
Aikido is really kind of a generic term. Inasmuch as there IS a naming convention in Japanese budo, most ryuha are identified by lineage, then by the broader art and any other details (like perhaps the area from which it came).
For example: Takenouchi Ryu jujutsu, Itto Ryu kenjutsu, Shito Ryu karate, Kodokan judo
(yes there are other types of judo), and so on.
So Ueshiba's aikido could be called Ueshiba-ha Daito Ryu jujutsu.
Aikido is a specialized subset of Japanese unarmed or lightly armed fighting arts, therefore it is jujutsu. It is derived from Daito Ryu, therefore the parent art is DRJJ. And it is Ueshiba's particular interpretation of that art, therefore, Ueshiba-ha.
He chose to call it aikido, sort of falling in line with Kano's rationale of using the term judo instead of jujutsu (although that distinction is really blurry, semantically and historically) after having called it Daito Ryu JJ, DR aikijujutsu, DR aiki budo, and other apellations. Eventually, he chose to break ties with Takeda and dropped the DR part in practical terms, but (as far as I know) never chose to rename the system formally. Aikido sort of stuck, despite it being non-specific.
There are folks in Japan (and elsewhere) practicing other jujutsu derivatives of DR who call (quite legitimately, I assure you) what they do aikido. Aikido, as a stand-alone term, is vague and sort of generic. Kinda of like saying 'karate' ... there are many variations, flavors and approaches and not all of 'em are Ueshiba-derived.
Is what _I_ do aikido? I practice a system of jujutsu, one that incorporates a concept we call 'aiki' and that contains portions of the curriculum we call aikijujutsu and aikijutsu (or aiki-ho -- not a typo, ho, meaning method). It is not specifically Ueshiba-derived. I tend to call what I do, budo, for simplicity. It is, more or less, a sogo budo -- a broad-spectrum, 'comprehensive' system -- that contains sub-systems of kempo (fist-method -- punch-kick stuff), weapons (sword, staff, and small weapons such as tessen and tanto) and the primary component: unarmed body arts.
However, my teacher spent some time in the late 50s/early 60s training with folks like K. Tohei and G. Shioda. Much of the taijutsu I practice today was flavored by those folks.
So ... I COULD call what I do aikido, if I wanted to (What did Pooh say about words?). And, indeed, Sensei would at times talk about aikido, but the curriculum I teach is broader than just the portion in which we explore the concept of aiki (though, arguably, it ALL encompasses aiki at some level).