I'm just brainstorming here, as I don't yet have my 5s to test... If it changes when you rotate it, wouldn't that mean the table or whatever surface is not level? Or perhaps both the table and phone are a little off and the errors add together at the worst point and subtract from each in the opposite direction?
My dad (lifelong carpenter) always taught me to properly test a level at the store, check for level, turn it 180 and test again, because that will show if its the level that's off or the surface you're testing. If both times the right side is exactly 1/4" low then the surface is off and the level is accurate, even though it looks off.
I'm not saying there isn't an issue, just tossing this out there as a way to verify how much exactly it is off.
Obviously if it were only the table you'd go from 4 degrees to -4 degrees as it rotated.