What "onscreen evidence" are you talking about?
Here you can see the doorway lines up with the two left most segments of the railing in front of it:

Yet here you can see the left side of the doorway aligns with the center of the gap behind the captains chair:

Also there is another shot in an episode where the navigation section is rotated at an angle from the viewscreen but I can't remember which one it is right now.
The only canonical evidence I'm aware of that even might settle the question is this scene in "The Cage" that was also used in "The Menagerie":
http://tos.trekcore.com/gallery/albums/0x00/thecage011.jpg
http://tos.trekcore.com/hd/albums/1x00hd/thecagehd0032.jpg
The original VFX are dodgy at best, and they arguably support not only the case that the cylinder immediately aft of the bridge does not align with the elevator doors but also the case that the helm module does not face forward. So, it's really inconclusive.
http://tos.trekcore.com/gallery/albums/1x11/themanagerie1_427.jpg
All that proves is that the bridge is actually a two dimensional plane set on top of the bridge dome.
