While the “why” in that book might be based on AZ, it probably came after it was shown to help. This is how it works in science as well. Experimentation usually precedes the theory.
Let’s not lose sight of the fact that the Issur of ‘Avoda’ Zara is exactly that, Avoda — worship. Actions based upon the ideology of a belief system on Avoda Zara is not worship. This is why, the Rambam explains Kishuf to be based on AZ, it is a separate Issur and has many Kulos, including Lihislamed, to undo previous Kishuf, and isn’t Yehoreg V’al Yaavor.