A human trained in the basic and fundamental technologies of his job can make decisions based on this training without ever having encountered or trained on the scenario in the past
Kind of a misconception. We have only two things going for us when we encounter a new situation - we can sort through past experiences to find ones that might seem relevant (and can do so fairly quickly, especially when the previous experience had a negative consequence, hence "learn from one's mistakes") and less important in the present context b/c a good computer could do so faster, we often can correctly calculate the near-term consequences of a contemplated action. As has been well mentioned, in this case relevant previous experience was lacking, by design.
The point about limiting human tasks to five is no doubt very important, but probably hasn't made it into the design rules. Beastly hard to implement when six very important things go wrong at once, and the flight computers haven't been programmed to boil them down to the root cause.
A few hundred posts ago I suggested that HAL should be tasked with warning the humans that he was starting to "worry" about a situation, and what was bothering him. That would give the humans just one thing to worry about themselves, before the cockpit was filled with stimuli, and with even a second's warning might plant the seed that would let them start the trouble-shooting on the right page.