As a footnote to what cxt wrote, he's right in that it may just be a marketing issue. Most people walking down your average street in America would have no idea whether Tang Soo Do, Hapkido, Mu Duk Kwan, Hwarang Do, Kook Sul, etc. are martial arts schools or some sort of Asian restaurant unless somebody in the know explained it to them. So, many of the styles of MA from Korea, and other countries sometimes, that have names that are less common than Tae Kwon Do or Kung Fu or Karate, will add "Karate" to their sign as an attempt to make it clear to the passers-by what the business actually is.
Ex: Joe's Hapkido Karate. Now, Hapkido is from Korea and Karate would be from Okinawa or Japan. But, your average Joe doesn't know what Hapkido is. But, any soccer mom in America knows right away what Karate is. So we attach the "Karate" to the end of it even though it's technically incorrect and a conflict in terms. (and, due to those political issues cxt mentioned, this is more likely to be done by an American teaching a Korean style than a Korean or Japanese born Master.)
I agree that it would probably be impossible to find an art that is still done today EXACTLY the way it was done when first created. First, as a MA Master grows, he finds new techniques or new ways to do them, or cuts some out due to ineffectiveness, etc. Then, under any given Master, you'll have instructors who will all teach the style slightly different becuase they have a differnt point of view. So, their students will look more like them than the origianl Master. And this continues on into infinity. Every instructor teaches what is most important to him. And every good instructor, I would say every good MAist, should grow, adapt, improve and adjust his techniques over time and improve them. If they're not doing that, they're falling off into obscurity. MHO of course.
~ This has already been discussed on other threads, but if you want to continue on this it might need it's own thread. I didn't mean to hijack the OP's thread.