Okay, this may get a little complicated, so bear with me here.
In the 70's and early 80's what is commonly refered to as Ninjutsu (refering to the Takamatsu Den arts, Togakure Ryu, Gyokko Ryu, Koto Ryu, Shinden Fudo Ryu etc) were all refered to under the generic title of Togakure Ryu. It is thought that that was primarily because the Togakure Ryu has the longest list of Soke, with 34, so that gave it the highest degree of respect. This is not dissimilar to arts such as Shindo Muso Ryu Jojutsu also encompassing arts such as Irraku Ryu Kusari Gama and Shinto Ryu Kenjutsu.
The name was later changed to the Bujinkan System of Martial Arts, with a focus on Ninpo Taijutsu, then changed again to Bujinkan Budo Taijutsu in the 90's. This was done to reflect the fact that Togakure Ryu is only one of 9 different arts that go towards to makeup of the Bujinkan systems, and the change from Ninpo Taijutsu to Budo Taijutsu reflects the fact that the majority of arts in the Bujinkan are not what would be considered "Ninjutsu" arts, although most have some connection.
The other reason the name was changed was due to the fact that the various systems are not commonly taught as separate individual arts, but rather the various principles of each are combined to make a unified approach to combat currently refered to as Bujinkan Budo Taijutsu. There are less-charitable reasons that could be listed here, but they are unnecessary, so I'll leave them.
So that's the name dealt with. As to what is encompassed in the teachings, commonly in the Bujinkan schools only the physical skills as listed. The other aspects of the Bugei Juhappan and Ninja Juhakkei are really just symbolic of training every aspect of yourself to as high a level as possible (or at least, that's how I approach the concept), but you can still find particular parts taught depending on which school you are learning from. For example, we have held workshops on bajutsu (horsemanship), Kyujutsu (archery), Intonjutsu (stealth and concealment) and more. So it could be taught, or it could not. But Budo Taijutsu as only the physical is a rather narrow interpretation in my opinion. The term Taijutsu refers to the body skills, so that is the physical, but the term Budo refers to the methods and approaches of the warrior, so that is much more far reaching to my mind.
When it comes to studying Ninjutsu rather than Budo Taijutsu, it can be done, but is not common. You would need to find someone who can, and will, teach you pretty much nothing but Togakure Ryu (pretty well acknowledged as the only completely "ninjutsu" system being taught, Gyokushin Ryu and Kumogakure Ryu being rarely taught at all), including not only the Densho material (Santo Tonso No Kata, Ukemi no Kata, Hiden Kata, Bikenjutsu etc), but also all the Kuden aspects to the art as well. Not easy. The Bujinkan teachings actually encompass much more than just Ninjutsu, so you are limiting what you would get out of them if that is all you are looking for.
To be honest, I don't think you've had much exposure to Ninjutsu, rather you have experienced Bujinkan methods, which may or may not have included Ninjutsu aspects to them. But systems such as Togakure Ryu are still not very well understood in the main (even after the theme of a year ago, it's just a very unusual art, and very different to systems such as Koto, Gyokko, or Takagi Yoshin Ryu), so the amount of exposure you would have had in the past is probably minimal, just so you know.
The Jinenkan focus on individual Ryu-ha study, taking each scroll in order, and learning the techniques the way they are written. So, yes, you will most likely learn the other aspects, but that will be quite a way down the track. The focus there is on the basics, so you will spend the first few years (at least!) just working on those, taken from various Ryu. But remember that each art you learn will be based on what your instructor has already studied themselves, if htey haven't studied Togakure, but they have studied Kukishinden, then you will be learning Kukishinden Ryu first.
The Genbukan was formed around 1984, and in the early 90's it was split into two sections, the Genbukan which focused on the Ninjutsu and Ninjutsu-related systems, and the Kokusai Jujutsu Renmei (KJJR). My personal feeling on this is that it is a reflection of the various teachers that Tanemura Sensei learnt from, and a way to more easily manage the various lineages he holds. He has since added to that another grouping known as Koryu Karate, as well as having a section devoted to the Amatsu Tatara, but that is only for high level members on the Genbukan if I recall correctly. You can be a member of just the Genbukan, the Genbukan and the KJJR, or more, and you will recieve rank in each of the various organisations as appropriate.
As to whether or not the "field skills" are taught here, again if you study the individual Ryu-ha, then that includes the Kuden, so yes. In the Genbukan/KJJR you can study an individual system after achieving Sandan. This is a great way to get the real depth of an individual Ryu, but remember that you are limiting what you get out of it if you choose a system as limited as Togakure Ryu. So most in the KJJR choose arts such as Hontai Takagi Yoshin Ryu or Asayama Ichiden Ryu, and in the Genbukan I think Gyokko Ryu is one of the most popular. Tanemura Sensei has recently begun teaching Tai Kais on single Ryu, and has one planned for 2010 on Gikan Ryu, so maybe a number of people will study this rare art after that.
Finally, on Richard's rank, the idea of him being a 10th Dan in Ninpo Taijutsu and a 14th Dan in Budo Taijutsu I think is confusing you a bit. For one thing, he is a 15th Dan these days, although that is really a 10th Dan. In the Bujikan the 10th Dan is split into 5 separate sub-levels, each named for a particular element (Chi, Sui, Ka, Fu, Ku), and for expediency and simplicity they are commonly refered to as 11th-15th Dan. So I think that the 10th Dan was given when the name used for the art licenced was Ninpo Taijutsu, and his later certificates came after they were changed. That's all.
Oh, by the way, any members from these various groups please feel free to correct anything I've gotten wrong here. I'm sure there's one or two things, I'm going from memory...