Hi all - I thought that might stir up some comment! : )
1) Judo came from Ju-jitsu, obviously - but calling any offshoots from Judo "Ju-jitsu" is like calling karate "kung-fu" because it had its origins in Fukienese and White Crane Kung fu, or like calling Aikido "Daito Ryu Aiki-ju-jutsu", Kendo "Ken-jutsu" etc etc.
2) The Brazilians calling it Jiu-jitsu still doesnt make it so. The historical reason for the name is that in the early days of Judo the term "ju-jitsu" was sometimes used interchangeably with the term "Judo", as Kodokan Judo was still fairly new on the scene and in competition with the earlier Ju-jitsu schools. Kano changed ju-jitsu into a new form, namely Judo, that new form was no longer Ju-jitsu as it had existed prior to that date, ergo any offshoots from Judo are reflective of its new technical direction and are one step removed from the original root art. So if you are going to argue that "BJJ is ju-jitsu because it came from Judo which came from Ju-jitsu" then you have to say in turn that the "Judoka are really doing Ju-jitsu after all, just like the BJJ people are, becuase THEIR art came from Ju-jitsu", and the whole comparison between the two set up in this thread falls flat!
Interestingly Judo actually does contain some of its original Ju-jitsu techniques for pure self defense use (see the Kime-no-Kata and the more recently created Goshinjutsu no kata)but these are unfortunatly seldom taught, a part of the decline of the Martial Art of Judo over the last 50 years and its transformation into a Martial Sport. In the first part of the twentieth century these were more commonly taught at the kodokan - hence many judoka (such as Maeda) picked up odds and ends of "self-defence" technique in addition to the formal Judo syllabus, without ever being members of a ju-jitsu ryu.All of this is very well documented. Once again, the BJJ syllabus looks like early Judo with a heavy emphasis on groundwork.
As I said before, BJJ is very good, can definitly kick some butt and has developed in its own unique way - but we need to be honest about the technical and historical realities of what it is.
My last comment in this rambling posting, is for those who seem to have a problem with me spelling the word "ju-jitsu" - if you really want to know, the offical standardized english spelling is in fact "ju-jutsu" these days, but has been spelled many ways over the years all of which are completely valid in my opinion as the Japanese dont use the roman alphabet anyway, so it is a moot point!
Whew, that was longer than planned! have fun trashing it : )