I've been asked this a couple of times lately. With the rise of mixed martial arts, kicked off by the UFC in the early 1990s, and before that the "Gracie challenge", Brazilian Jiu-jitsu (which we used to call Gracie Jiu-jitsu) is now better known than Japanese jiu-jitsu.
A similar story pertains to Karate. Many people think of Karate as Japanese, but it was introduced to Japan from Okinawa in the early 20th century, and before that was adapted from southern Chinese martial arts, and even known as "Chinese hand" in parts of Okinawa.
You have to draw the line somewhere. So I say:
- Kung fu (Chinese boxing) is from China
- Jiu-jitsu is Japanese
- Karate is Okinawan
Japanese Karate is an offshoot of (Okinawan) Karate. Brazilian Jiu-jitsu is an offshoot of (Japanese) Judo. Judo is a daughter art (along with aikido) of Jiu-jitsu, and they are all Japanese.
Both Jiu-jitsu and Karate, although influenced (and maybe derived in large part) from Chinese kung fu styles, have had enough time to become more than offshoots. Plus: the names were changed.
In the end, the history doesn't necessarily matter as much as the content. There are only so many ways to move the human body, and most (all?) ancient cultures featured some form of wrestling, boxing, and weapon-use, and must be the forebears of all martial arts. Today martial arts have significant areas of overlap.
Getting back to the original question, it doesn't bother me. Such a question is usually evidence of innocent ignorance on the part of the questioner, and nothing malicious. Most (all?) martial arts practitioners tire of being asked how their "karate" or "taekwondo" (or whatever the flavor-of-the-month style is) is going, by well-meaning but martial arts illiterate family members or friends, who are merely trying to "show an interest" or make small-talk.
Interestingly, now that there are so many schools teaching Brazilian Jiu-jitsu, Japanese Jiu-jitsu may be gaining in cachet because of its relative scarcity. I do get enquiries from people specifically seeking it out, and that's often a good sign. On the other hand, some people assume that all Jiu-jitsu is Brazilian Jiu-jitsu, but these are quite quickly dispelled.
I wonder how many people think that soccer is originally from Brazil, too.