Joe Staten, cinematic master of all things Bungie, dropped a couple coppers in the coffer over at HBO regarding a note in their Halo Review; it seems that while most in-engine cinematics do accurately keep track of what's gone on in the environment around you, the weapon the Chief is holding isn't one of them:

The only consistent gamestate error during the cinemas is the fact the Cinematic Chief only shows up with the assault rifle rather than whatever the Player is carrying. Unfortunately, it would have taken some special code and scripting to rectify this error, and other things were more important--like making our ship date :')

Thanks again to Louis Wu. Join us next week for another exciting episode of Assault Rifle Theater.