Gerry,
You've pretty much summarized the whole thing. But, what is pretty much a generic term today in the west was not in the recent past, and therein lies the friction.
Adding to the friction has been a heap of people, mostly outside Japan, wishing not only to separate themselves from modern Aikido but also to jump on the "jutsu" bandwagon because they want their art to seem tougher, even if it only amounts to their adding a few judo/karate/misc techniques to their basic aikido repertoire.
There are cases inside Japan where care was and is taken to AVOID using the aikijutsu name, BECAUSE it is not considered generic (even when one or two generations away from Takeda!), but even today there are some dubious organizations there that walk/talk and look like and advertise "it" but fail under scrutiny, because they fall under the previous category...rougher aikido with punches/kicks, or even mimicking the original in shape and movement but without an understanding of the underlying principles. Unfortunately for the average prospective student, they can't tell the difference, and we can only hope they start a topic on a martial arts message board asking questions. Whether or not they care about the replies is moot!
What it's come down two in the last thirty-plus years or so, especially since video tapes became a common way to share or sell anything interesting, is "pollution" to put it bluntly, and more than ever the latin phrase "caveat emptor" ("may the buyer beware") is fitting.
Devon