Kind of misleading what you originally wrote.
From the link:
"Mr. Kitamura really respected and honored the original work, so like the helicopter, the chopper flying up, the scene there is pretty loyal to the original scene. But then we said, "This isn't it. If we're going to have Mr. Kitamura do it, we want him to do it his way." So what you're not seeing now, but what you'll see later on in the game is totally different. You'll be shocked."
So yes, originally Kitamura stayed true to the original. And yes, Kojima rejected it. But Kojima didn't tell him to make it more over the top, he just wanted Kitamura to do it the way that he (Kitamura) wanted to. It just so happened that Kitamura likes things to be over the top. I've only seen one of Kitamura's works (Versus), and I haven't played Twin Snakes, so I can't comment on whether or not it follows his style, but from the interview, all the cheesy cutscenes were the work of Kitamura.
OP: My favorite MGS game is MGS3. The only real complaint I have about the game is that while the boss fights were great, the bosses themselves weren't all that interesting.