The main reason for the falling out, at least in her opinion, is that Kojima gets paid a salary, and doesn't make any profit share on the game. He gets paid a certain amount no matter what, and he was spending so much money and delaying the project, and adding all these features and making sure the game was the biggest and best thing it could be, and Konami was unhappy with that because [delaying] has no effect on him. He was spending the budget on this and that and upgrading the Fox Engine and then delaying further because the engine wasn't ready, and Konami wasn't happy with that because he gets his salary and he takes a more traditional "Japanese man" approach by not taking a profit share. So in doing that, he gets a little more than a game creator would but doesn't take bonuses from the game selling well.
In her eyes, Kojima's a fantastic creator, and probably the best creator of his time, but he doesn't have a strong business sense like Konami would like him to have. Where instead of, for example, cutting corners by lowering foliage resolution, he wants to make sure everything looks as good and polished as possible. She said they paid for her to write 30-40 songs that ended up not being used, and he'd tell her to write another one, then another one, then another one, because he settles for what he likes and has a good mind for what people want to see and what people want to hear.
She's worked directly with Kojima for the music before so she does have some insight, and personally believes that the music has suffered in MGSV because she's not a part of it, because they couldn't afford her. So instead of paying her to go to all these people and recruit them for the music, they chose to remove her from the equation and go to the people directly.
There's two ways to look at this. First is the stance that Konami simply didn't want to give Kojima the funds to make the game to the best of his ability because it'd be too expensive. Konami isn't in the best financial position right now, so putting all of their funds into something like Metal Gear Solid V would be a potentially unnecessary risk.
The other way of looking at it is that Kojima was simply pissing away Konami's funds on things they didn't feel were necessary, and he was safe to keep stretching out development for as long as he wanted while still drawing a salary.
