There is SOME stuff going on with that skyscraper and the floor which no one can reach. And the door that’s open a certain amount of time. Morpheus, Neo and the Keymaker enter one of those programmer’s backdoors and meet the Smiths.
So the Architects room is in a completely different area.
Something just struck me! As JediHDM points out Neo must’ve flown quite the distance, to get from the Architects room, through the corridors and out in the skyscraper. Was that a trap? Was that a fail-safe mechanism? IF the One choose to return to the Matrix there is ONE other way to get him to the Source. Kill him. All programs that are killed in the Matrix return to the Source (also digital selves, avatars, they ARE still programs). It’s not disallowing choice. It’s simply cheating.
Neo was just too fast. And he was too fast for a reason. Trinity.