Falcon - I understand what you mean about the mystery of whether Choi actually studied with Takeda since niether his korean or japanese name was listed in the school records. I definately think that if he did study it was private between him and takeda. The other story I undersatnd is that Choi watched all the classes and practiced on his own. Helio Gracie said the same thing. I don't know but I sure as hell couldn't learn an art by watching especially if I had to make sure I was not seen.
Choi was basically a manservant for Takeda so even with the racism of the japanese (towards any no japanese especially Koreans) It is possible that they could have bonded and Takeda showed him the style and said keep it to yourself. But after Tekada died there was no reason to be secretive. That's just my opinion I really don't have facts of course.
Regarding Yu Sool (which I think is Korean for Jujitsu) don't quote me on this , but I don't think Choi studied Yu Sool I think that his first dojang he called the art Yu Sool, actually quote me I remember this from an article, the sign above the Dojang was Yu Sool. Then Choi went back to the korean arts and combined his knowlege of Daito Ryu with Tae Kyon (definately don't quote me on that one I really don't remember the korean art)
Hapkido doesn't have ground fiighting but I guess it depends on what your instructor trainined in, the Hapkido instructors I have seen have training in TKD or Judo or JJJ. I went to a Aikido dojo once and after I told the instructor I studied Hapkido he said "so why study Aikido its the same thing" but it not, in my opinion...maybe I askeed too many questions.
Interestingly, I was told that Hapkido is translated as Aikido in Japanese. Does anyone know if that is true?? If so, I wonder why that name was chosen by Choi.