Bucket fill - fill whole selection also affects pixels outside of selection

[rich2005]

With the procedure you are using you have lost most, but not all of the anti-aliasing. That is the semi-transparent pixels that give an impression of smooth edges. The bucket fill just fills those according to the transparency.

Without going into "why" you do not want anti-aliasing. You can remove the remnants with Layer -> Transparency -> Threshold Alpha The setting, almost but not quite maxed out. I put in a colored layer under just to make things a bit more obvious. Before is in the box.