Okay. You are a shadow group, composed of politicians, corporate big shots, rich people, etc.
You are in a dangerous time. Basically, WWIII. European countries are warring with one another, USA takes over Canada and is in war with China.
The world is potentially on the brink of nuclear war.
What do you do? Use all the power in your organization to survive, or limit yourself?
What would a person do? If say, we were headed towards nuclear war, I would make a list of things needed to survive. Make preparations. Because it is in my nature to survive.
If you did..nothing. The odds are you will not survive. If you did just one thing, I collected water! The odds are you will not survive. Do a great many things, and still, there exists the chance you will not survive.
This is why Enclave had multiple plans. It increases, but does not perfect, chance of survival.
What you are suggesting is that the Enclave was a large influencial survival group. What purposes does a "corporate bigshot" have in an organisation which is planning for an event which would render him useless as an asset? What you're suggesting is that the Enclave was a cabal of high-ranking people whom built fancy long-term survival shelters, why not just have Vault-Tec build a private vault? You believed that the same people controlled Vault-Tec and built the experiments but if immediate survival is the only goal why go in for all the shadowy [censored] at all? What is the point? If you're going to say something along the lines of conquering the United States then how does that work? Why are the remains of the DoD, Congress and such all in their own centralised networks and locations and then there's a motely group of different professions on an Oil Rig in the ocean calling the shots? Again, what purpose in this senario do corporate executives and just "rich-people" have - having neither any authority, money or assets anymore? Why is it easier this way than having the people in this "group" just have a 100% fool-proof way of being the proper governmental bunkers, those are pretty spread out after-all.
Of course all of this is equally as plausible as the remnants of the government simply regrouping after the war (an event which
actually happened)and becaming the Enclave from that point on? No lingering questions, no [censored] motives, no insanity, just a reasonal explaination; the Fallout U.S. Government were always amoral [censored]s anyway so why Vault-Experiment? Why Mariposa, why Big MT, there's a good explaination for the Vault Experiments - something in the U.S. Government thought that there was probably some valuable research to be gained here so just set the thing in motion, it has a precident and motivation. Hell in Vault 21 it says that it was no secret that the Vault had ulterior purposes in testing societal concepts, a perfect cover operation. But no the Shadow Goup did all this because they had their own private project that required such research... somewhere... in a future game maybe..
Maybe the Enclave was actually a bunch of right-wing pro-American extremists, maybe they were a cabal of corporate and legal big-wigs, maybe they were a secret society like the Masons or a purely American Bilderberg Group; there is no evidence of one over the other and you could probably argue whatever you like because there's nothing to say what's right or what's wrong with your theory.
EDIT: Again what's the most likely source of the Enclave's name? That it was the official name of the Oil Rig (again, sourced) that they were based on and they adopted it or it was the shadow government signing it's work in the official records of the damn Depertment of Defence. Doesn't that suggest that the Oil RIg is the main Enclave base then, being named after it? So who opts to stay in another location when the leaders of the Shadow Government have gone as far as to brand this base with their own name?
EDIT2: I don't defend this viewpoint because it lends creedence to any more of my musing on the Enclave, the supposed origins of the group really have no bearing on whether the group is a continuation (unless of course the Shadow Government had the power to have the Constitution legally amended by Congress to suit their eventually take-over and have self-preferencial emergency laws passed to give themselves power - yet they still want more power!). It simply makes more sense as a backed-up theory. This is, if you will, a societal study of my own to determine why people but into such a convelueded theory - I have my suspicions anyway.