The outside-width of the rim may also vary at different spots on the rim (due to hitting pot-holes and kerbs in the past). Take the tyre off the rim and measure the outside-width with some vernier calipers. Then slide the caliper around the entire circumference of the rim and it may get stuck at a spot that's wider than the rest. I've squeezed these wide spots back to parallel by clamping the rim inside a vice. Do a little at a time and re-measure with the calipers.