I think that, when you look at Peace Walker... the two post-credit conversations were both thrown in there in order to tie things together with MG1 in case there wouldn't be a sequel. If Ground Zeroes didn't exist, you could maybe take the "Call me Big Boss" conversation to allude to his future of returning to the United States now that he's gotten over the Boss and and is no longer ashamed of that title and can make his move. And you could take the "This is Outer Heaven" speech to be alluding to the Outer Heaben Uprising with him rebranding MSF into Outer Heaven, which i'd say is a logical assumption what with Hayter being told to make his voice even raspier in that speech than the rest of the game implying time had passed (more than Ground Zeroes now implies).
But now that Ground Zeroes & Phantom Pain exist, we know that speech now fits between the end of Peace Walker and Ground Zeroes as MSF is destroyed a few months after the Peace Walker Incident whilst they're still called MSF and they never got to the point of being "criminals, terrorists" or being actually known as Outer Heaven until Diamond Dogs. I think both conversations might have been put in there because they were intended to close doors, and of course the problem with that is when you create more sequels and reopen those doors later... you have inconsistencies and end up wanting to backtrack so the arc planned for the new game can go even smoother, and now we'll need an ending in Phantom Pain that is even more elaborate in showing the beginning of the Outer Heaven Uprising and Snake becoming the "Big Boss" of those MSX games.
I guess what i'm trying to say is that it's probably just be a retcon, at the end of the day, as Kojima said he's choosing to have some minor inconsistencies for the purpose of making the transformation in Phantom Pain even better. I mean the main thing that mattered with Peace Walker wasn't that he wanted Kaz & Friends to start calling him Big Boss but that he got over the Boss finally, as long as the story still reflects that I won't be too mad about it.