There was a much disputed article sometime last year that talked about how gameplay tells one story, and cutscenes tell another and what horrible disbelief arises when the two doesn't match.

I find Portal to be the absolutely best example of how to tell a story solely through gameplay and enviroments. And for me it jives much better than telling through cutscenes and dialog boxes.

I really prefer telling stories within my mind than being fed the stories. Since I make stories with my mind all the time when I'm playing anyway.

Portal is a wonderful example!  Everything from when you first wake up in the room to the very end is full of great story!  Valve in general is just really good at this stuff.

It's the degree to which the story details are filled in by the author/director/producer/developer vs. how much is left to the imagination. It's not necessarily about the amount of words or images but instead about getting the consumer to use their imagintation

Some examples:

Hemingway's "The Old Man and the Sea" or "The English Patient"
Star Wars OT or PT
Final Fantasy or Half Life
Mozart's Operas or Twinkle Twinkle Little Star.

As far as applied to this example, I think it has more to do with how you like your stories.

Per the definition of storytelling, the cutscene is objectively better in every possible way.

While you are right about non-interactive entertainment, it suddenly becomes completely different when you actually control parts of the story. When the parts that you control differ drastically from the parts that the director controls, the effect completely ruins all attempts at immersion and setting the mood. Yahtzee had some points about that in his latest review of Siren: Blood Curse.

In Final Fantasy, it doesn't matter how strong you get, some fights you loose, simply because the script requires it. It frustrates and takes the believability out of the story. The examples are endless. This schism doesn't appear in traditional storytelling at all, and it's the biggest problem, I believe, that storytelling in games is facing today.

That's because it's much harder to tell a good story in an interactive medium, not that it's easy in movies and books.  Personally though, that losing a fight in FF thing never really bothered me before yet you say it takes the believeability of the story.

But why is it so much harder to tell a good story in an interactive medium?

You say it isn't because of the the will/actions of the player colliding with the will of the storyteller. If not, then why? What is it that makes interactive storytelling so different?

Why do most people like picking on FFXII?

Because developers are still finding new ways to tell a story in a video game.  Also, even it though it doesn't apply to every game, some games offer choices that affect how the story plays out.  Implementing something like this is far from easy.  I don't think the developers of Heavy Rain are having it so easy either.  There is definitely room for linear storytelling.  Heck, most video game stories are mostly if not totally linear.  I find that it's easier to accept that losing a fight in FF thing to me due to suspension of disbelief.  Either I am bad at knowing when my suspension of disbelief is broken or yours is a lot easier to break than mine.  Breaking mine would probably take some distracting elements such as laughable voice acting and have severe plot holes.