When most of our birds were named, the scientists shot them and held them in their hands. The red-bellied wp in fact does have some diffuse red in the lower belly area. It is not so prominent as a field mark, but in the hand it is quite different from what other wp's have. You can sometimes see it when they perch at a feeder, there is a hint of it there above the undertail area in your second photo. Some birds show it more prominently, but it is never as sharp as the red on the head.
