In Cycles, does distance from the camera affect noise?

I have been following all the tips and techniques to reduce noise that I can find, but have not been able to eliminate noise at the back of my scene, which is basically just a hallway.

The figure and objects near the camera come out crystal clear at 2000 samples, but the figure at the far end of the hallway is always noisy regardless of the amount of light I add.

Much of the hallway is in slight shadow, but I have multiple lights (sun lamp through windows, cove lighting above, a light plane blocked to be a spot to light the figure at the back, slightly reflective arched ceiling, glossy floor tiles).

Caustics turned off (turning it on doesn’t seem to make a difference in noise.)
World AO turned off. (A couple of materials have AO nodes.)
Limited Global Illumination from a texture.