Here are my thoughts:
1. Why can't they use the values for the factors specified by the design (JMP)?
2. The assumption is, in experimentation, that if you set a low level (e.g., -1 coded) and change the level setting and go back to low level, -1, that level is identical to the previous level 1. This greatly simplifies the analysis and allows for assignment of higher order terms easily.
3. The reality is, variation exists in everything, so one strategy to overcome the within level variation is to ensure the between level variation is large (e.g., bold level setting).
4. If you want to do use the actual values, depending on how much they vary from the specified level setting, you might lose the ability to assess higher order terms like interaction effects. If they are not that different, probably doesn't affect the analysis too much .
I'm not sure I would consider your advice "correct" or just one way to analyze the data. I would try analysis of several experiments using the coded values and the actual values and see how the output of the analysis differs.
"All models are wrong, some are useful" G.E.P. Box