I don't pretend to understand exactly how it works, only that it does work. Customer Service Magic is what happens when you struggle for a long time on trying to get something to work without success. Frustrated, you call the help line knowing 'oh, customer service is never helpful, I don't know why I'm bothering.' The agent on the phone doesn't actually do anything extraordinary or special to your exact circumstances, but as a result of having called, you will suddenly be able to do whatever it is you were trying to.
Happily, this phenomenon also occurs in the tech field. Often, my employees will come to me with some question, and sometimes I don't even get to sit down and take a look at the problem when they figure it out. These instances make me think that CSM is just a tool to help our brains catalog and revisit problems from new perspectives.
Other times, while helping someone and trying multiple solutions in vain, some permutation will click into place, and suddenly, despite doing steps you were sure you did exactly the same several times previously, the problem will be solved. Unfortunately, this sorts of solutions are only useful once, because without understanding how they came to pass, the next person to encounter it will have to go through the whole ordeal themselves. This sort of situation makes me think that CSM introduces new variables that can cause someone to deviate just enough from their previous attempts to hit on one that works.
I myself have been on the receiving end of Customer Service Magic. I don't remember the precise circumstances, rather just the feeling of relief as I realize that my issue is gone and I don't actually have to stay on the line for an hour trying to fight my way through scripts.
I don't know whether CSM only occurs with customer service representatives who feel a passion for their product or service, or whether it can happen with any wage slave. Maybe the ones who are passionate and care about getting good results for their customers are the ones who notice it?