Forward and backward stepwise regression always terminates with the same model. Adding terms or removing terms does not affect the values of coefficients in the model. The model can have more terms than absolutely necessary. In general, coded units are preferable. It is rare that a physical simplification like the one in this article actually happens.
Coded units are especially useful in the analysis of screening experiments.
In these studies the ability to compare the coefficients directly supports the screening goal. You want to keep the big effects and screen out the small ones. Using coded factors makes effect size comparisons simple. Though the parameter estimates shown in Figure C appear quite different, they yield exactly the same predicted values. Regression predictions are invariant to changes in scale in the predictors.