There's a good book (albeit, a bit repetitive as you read it) about the fall of of GE. If I remember correctly the book basically confirms what you said about Immelt inheriting a lot of problems that were hidden behind accounting complexity at GE.

https://www.amazon.com/Lights-Out-Delusion-General-Electric/...

Not that Immelt was a star either, but he he wasn't the person who created a lot of these problems.