Most of the cutscenes are indeed filmed "in-game".
An obvious example of this is the scene at the beginning of the NMPD HQ level where the pelican is chased by banshees and Romeo shoots at them with the sniper (the level even starts with three shots having been fired from his clip).
A less obvious example can be taken from Halo 3. If you remember the scene where the characters have gathered in the Elite flagship to chase the brutes to the Ark, they're in the bridge of the ship talking about saving cortana and kicking covenant ass and stuff. That scene is actually filmed "in" the level "The Ark", and you can even get into the bridge where it's filmed, which is hidden inside a mountain. There's a youtube clip here showing you how to do it, if you care to.
http://www.youtube.com/watch?v=zumz4Ie5wvYSo, it stands to reason that most, if not all, cutscenes are filmed somewhere "inside" levels, though they're often cleverly hidden behind scenery.
An exception might be scenes that have their own "level." An example of the is the "Prepare to Drop" opening scene, which probably stands alone from the other stages. Another example might be the post-credits ending cutscenes, which likely have their own "levels" as well.