Everyone is arguing here about whether or not 1st or 3rd person is inherently more immersive, but ALL of you have it backwards. Camera systems are means to an end! Immersion is the result, not the starting point, and any route can lead there if taken carefully.
Limbo was immersive, and it was a 2D sidescroller. It used an effective artistic style and palette combined with thematic reinforcement to immerse the player into the world it created. I could say something similar for Okami. I could say something similar for Portal.
Portal could have been 3rd person, but it was decided that making it 1st-person would make for a more immersive game. I'd agree. It made it that much more psychologically effecting to burn the companion cube. But what about a Zelda game? Imagine Wind Waker in the 1st-person. I bet that would result in a much less immersive experience.
If a game is immersive, it isn't because of its camera choice. That may be a factor, but only in tandem with the rest of the design aspects of the game. Replicating real-life is often irrelevant.