The MGSVTPP timeline says that BB1(Naked Snake) is forming the Outer Heaven Nation, while in the game the Mother Base BB2(Venom Snake) builds is called Outer Heaven as well. The timeline then says that Solid Snake is deployed by BB1 against Outer Heaven, but it's not made clear if BB1 is doing so because he genuinely wants BB2 taken down, or if he's sending in SS to maybe extract Gray Fox but then pull out without succeeding in taking down BB2 (the original timeline where he doesn't expect SS to succeed.)
In favor of your vision is BB2's clearly damaged mental state, particularly in that last cutscene, and the way BB1 is much more erudite and vocally respected in MG2. However, I'd argue that BB1 is also slipping into darkness, albeit a much more cold and calculating type of darkness: unleashing a brainwashed body double to rescue your friend and take revenge for your loss while you continue to build a private army to wage a war, isn't any better. And we know that Miller said he would oversee BB2 and try and turn him against BB1, and we only see Miller working against BB1, possibly implying that he doesn't begrudge BB2.
I'd prefer that BB1 and BB2 are still working together in MG1, and that the events play out in such a way that both men are ultimately doomed by their stubborn nature. So to me, BB1 sends SS to extract Gray Fox, and sends a briefing tape to BB2 to allow that but to defeat SS if he goes farther. When SS pushes through and succeeds, BB1 tries to sabotage his mission as in the original game, thus outing himself to the Patriots and possibly Snake as well. Now that their cover's blown, BB2 tries to take SS down, possibly against the advice and pleading of Miller. BB2 gives a good fight, but falls.
Now, Miller has even more reason to turn on BB1; while his old friend abandoned him and tried to make him a pawn in his war against the Patriots, he also sacrificed the man who actually rescued Miller and helped him get revenge. BB1 can now rebuild his army, but with a bit more openness about his identity, and thus a higher profile and dignity in his defeat.
We don't see it or play it, just read it.
