I agree with this.

There are two main fastening points. We've been discussing fastening the arms to the brake frame. The brake frame has a spring that holds the calipers in a certain orientation. The other fastener holds the brake frame to the bike frame. To adjust centration on this type of brake, you snug that nut up a little bit - not too tight. You then use some leverage to push the spring I mentioned to center the brake. What we used to use in the bike shop was a screwdriver under the bike frame crossbar on the high side. You could push down on the spring and center the brake frame. Then tighten the nut. It turns out that your brake frame was in proper position, and once you straightened the calipers and reinstalled them, it was serendipitous that your calipers were set up correctly.