»Does Neo really choose the left door ?«

I just finished watching reloaded again and it kind of got me wandering.

At the end of the scene with the Architect when Neo says, "If I were you I would hope that we don't meet again". It looks as if Neo is putting his hand out to open the left door but we don't actually see him walk through it.

The next time we see Neo he bursts through a door (not opened), this is clear as there is a close up shot of the door handle and you can see the paint on the door bubbling up but the handle doesn't move. I think that in this scene he flying out of the room with the architect because you can see the bright white light coming from the doorway.

Is it possible that Neo chooses humanity over Trinity and his comment to the architect is in the context that he is pissed because he has to let Trinity die ?

I know your probably thinking "but Trinity lives". That's true but she does die first and is brought back to life by Neo, so in a way the Architect wasn't lying.

My theory probably has many holes but I would like to know what you think..