To be fair, I don't think Gamebryo is the cause of these issues.
Going back to Morrowind, a source from August, 2001 on Bethesda using NetImmerse provides this info: (Can't post source link but google should provide it to you)
We can see that NetImmerse was mainly used to provide an art pipeline, cross-platform support and some smaller features that all engines have. So, we can assume that from the get-go a lot of it was already rewritten. Especially since Gamebryo is not an open world engine, open world engines require a very large amount of system-related work to function correctly. Rendering, terrain, AI, Scripting and Physics were all possibly written by BGS for Morrowind.
From here, we can only assume the differences between the engines increased, the art and animation pipeline remained the same for Oblivion, but the rest changed around it. I'm betting that Materials and Visual Effects system became BGS-made around this time.
In Fallout 3, we have of major note a new animation system, further more removing it from its origins. I also estimate rendering and lighting were changed as well.
In Skyrim, we have huge rewrites: Havok Animation is implemented, Rendering, Lighting & Physics were re-written from the ground up as well as other major changes across the engine, including an entirely new in-house Foliage Creation & Rendering system.
So, as you can see the engine has never really been "gamebryo", for the most part any bugs have been from BGS tech. Now, I'm not saying it's because all of their programmers are terrible, open world games, especially on this scale have a large list of technical problems to solve.
In terms of branding, I think it does deserve the title Creation Engine, Gamebryo is seriously only really used for very minor and old systems, most of it is BGS tech. For example, Valve's Source engine still contained Quake 2 code, if they're not removing the code it means that removing it would have a negative effect on the whole scheme of things.