I can honestly say that the statements about the map being divided into cells just like oblivion, having almost the same map size and cell size as oblivion, the overall appearance and details like houses still being in seperate cells to me all points to it being pretty much the same engine. For those who have experienced working with other engines you might agree these details do seem to point to it being the same engine...
These have nothing to do with Gamebryo as far as I'm aware. There's nothing in Gamebryo that forces all games to be "cell-based", exterior-interior separated, open world RPGs. These features all seem like design decisions made by Bethesda for most of their modern games and lie separate from Gamebryo, which for all we know just managed to get the rest of the engine onto a screen. A lot of their code in Oblivion does have "NI" (NetImmerse, pre-Gamebryo) in the class names, though, so it does appear that either their code was originally based off code from when they relied more heavily on Gamebryo itself, but had since modified it, or a lot of it was straight from Gamebryo, who still used the "NetImmerse" title in their class names. Either way they seem to have still had some pretty old code, given that calling class names "NetImmerse" dates it all the way back to Morrowind.
Ways to detect if the new engine was stripped entirely of Gamebryo may be difficult. They're likely comfortable with their workflows from Fallout 3 and Oblivion. They may keep the NIF format, similar INI options, they may have kept the class names of all the functions similar but stripped out most of the old code and put in their own.
In any case, what Gamebryo did for Oblivion/Fallout was probably not very important for modding or modders. The creation kits were all Bethesda's own doing, even the ESM/ESP/BSA formats may have been theirs from when they first did Morrowind, I don't know. But I would say "probably". ESM/ESP = Elder Scrolls Master/Plugin ... BSA = Bethesda Studios Archive ... But that's just a guess on my part. Gamebryo mostly had to do with portraying everything on screen, and not much else. The scripting, AI, whatever else was all Bethesda's doing. I'm not sure why you thought Gamebryo was "rather garbage" but people say this a lot. I would agree that Gamebryo was certainly limiting... It certainly didn't seem to allow for very good animation, the lighting system was crap, etc. But I think a lot of people thought Gamebryo was inherently glitchy, or messed up, which I don't know where people get this myself.