This is really puzzling. I tried it on my MBP, but what I'm seeing is when a texture is 4096x4096, it seems to be downscaled to 2048x2048 when in iPhone build mode, otherwise it displays correctly, when it works.
Can you check a few things just to rule things out -
1. On the atlas texture, the max size is 4096 and there are no platform overrides for whatever platform.
2. In edit > project settings > quality settings the texture quality is "Full Res" (You have mentioned this before, but just checking in case)
3. Can you drag the texture onto a cube and see if you see the same results - you should, as I did above too.
If this is whats happening, then this could be a bug / known issue in Unity.