Difficulty 67 explains treatment through back shu or front mu points in following way: if disease moves towards yang, shu points should be punctured; if disease moves towards yin, mu points should be used for the puncture.
Only acupuncture pulse diagnosis may show this movement of disease towards yin or yang. Herbal pulse diagnosis can't do so.
As example liver meridian may be dominated by cold, water movement, yin is increasing, pulse becomes deeper, disease moves towards yin, front Liver mu points should be used for puncturing and back Liver shu points may be added for moxibustion to increase yang, decreasing yin.
Another example if the liver meridian is dominated by dryness, metal movement, yin is decreasing, yang increasing, pulse becomes more superficial, disease moves towards yang, front Liver mu points should be used for moxibustion to increase yin, decreasing yang; back shu points should be used for acupuncture to decrease yang.
As you may see use of back shu and front mu points are quite different in classical acupuncture comparing to modern TCM, and they use may be confirmed and explained through the acupuncture pulse diagnosis