I think the kind of immersion that one experiances playing AD&D 1E will largely depend on the personality and imagination of the player (despite its creators intentions).
That said, I think Storm Raven is correct. Check out pg. 104 "Negotiation" "Most DMs love communication and neg. for this allows them to assume an active role in actual play. Your ref. will assume the persona proper to the creature your party is dealing with be it shy or hostile .... "
I think its logical to assume that if your DM will assume the "persona" then you, the player, are supposed to as well. I know when I first played the game, not really knowing any of the rules (thats the DMs job) all I was left with was immersion. Not only seeing and smelling and touching the world in which I explored, but talking, hiding, running...all the things one does in real life, and in a very fluid way. The DM might be sitting back applying the rules and rolling to see what happens, keeping track of "moves" and such, but lets face it...the first time you played this game you were "there". At least I was (and the biggest loss to D&D was going to the D20 system where players feel like stacked sandwiches and know the rules backward and forward). The fact that your PC was usually some average Joe (no bull strength and tumble and what have you) made it that much easier to relate to that character rather then just watch it (this is similar to reading "The Hobbit" and LOTR) as a kid its easy to relate to the halflings, there small and weak like you. But the elves, Gandalf, even Strider...forget it.
Now there is a difference between watching your character and being your character. I think someone like Foster didn't see from the eyes of his character, but rather watched it and made it act like a puppet. I on the other hand am the kind of player who "is" that character, seeing out of its eyes. That doesn't mean I behave at the table like some out of work thespian actor, far from it. I only talk in character when the DM forces me to (usually responding to an NPC). Otherwise I say "my guy does this or my guy does that", and I never communicate with fellow gamers at the table "in character" its still "I'll trade you this +1 ring for your +2 shield" not "Horthak, what sayith we make a bargain...bla bla". I find this kind of "acting out" works well online however..but at the gaming table...its just creepy :\ .