Let me try to explain this without too much technical detail. The problem with the laptop was that it didn't boot, and this problem was caused by repeated attempts to power it up on an empty battery. The attempts made by our Tech gave some interesting insights in how these people are trained. What he basically did was attempt a series of solution procedures that he selected on the basis of association with the problem. Our two "symptoms": computer did start up, but got stuck in the process, and something wrong with power. In this case, the power was a red herring: the real problem was the computer not booting. But before acting on either symptom the first procedure the Tech did was to hook up the computer to a standard hardware test. This showed up no problems with power nor hard disk, but did show up a problem with some sensor: the second red herring. This is something that sometimes happens in the medical profession as well: you go to the doctor with a problem, they do a test, and you end up with two problems.
As a result, the Tech went backstage to try and push all the sensors back in place. An hour later he was back from doing this, with no result. No surprise in retrospect, because the sensor couldn't possibly have been the problem. He then started going through a whole bunch of procedures related to power, up to verifying that our battery was past its expected lifetime (which we already knew), and verifying that the power adapter was indeed working fine.
In the end he did not solve the problem, but I walked away with a pretty good idea what was wrong and fixed it when we returned home.
The point here is not to criticize the Tech. He was obviously not a genius in the normal use of the word, but he was trying his best, but probably on the basis of the wrong strategy prompted by the wrong training. His approach, to reiterate, was to throw solution procedures onto the problem based on associations with the symptoms. What he should have done is try to reason out what possible causes there are of a computer not booting. Defective hard disk? No. Will the computer boot from another source? Yes. Then there must be something wrong with the OS: it needs to be fixed or reinstalled.
So why is this story important for multitasking? In order to be a good multitasking, your skills have to be flexible. When I am cooking from a cookbook, I have to pay close attention to the order of the steps and the ingredients I need to gather. I cannot really multitask very well while cooking from a recipe. But when I am not cooking from a recipe, I can happily watch the news, chat with people and do other things. So why is that? When I am not working from a recipe, the representation of what I need to do is flexible, and I can immediately respond to what I see happening in the kitchen with the right action. But when I cook from a recipe, I have to repeatedly consult the recipe and check what step I am in and what to do next. In the recipe case, I have to maintain a mental representation of the state of the food, and can therefore not afford distraction, but if I cook without recipe the world is my mental state.
Training in terms of learning procedures is very common. I carried out some studies with airline pilots who need to program their onboard computer, and are also trained in doing this by memorizing procedures. The airplane computer is a masterpiece of user unfriendliness, so some pilots despair in using the thing, and training on it is sometimes compared to "drinking from a firehose". The main reason why pilots have so much trouble is that they do not understand what they are doing. They are just carrying out procedures (did someone say "Chinese Room"?).
Our lives are full of procedures: look at any electronics manual, medical practice, pilot training, probably Apple Genius training, etc. But opaque procedures turn us into automatons, and blunt our capacity for creative problem solving. And that while it is not so hard to change things. In our pilot example, just adding an explanation of what each step did increased performance on the task tremendously, and also allowed subjects in the experiment to come up with new procedures for problems they were not trained on.
So what makes a true Genius? If I only knew... But improving training and instruction may be a way to make us all a bit smarter. And better multitaskers too.