Interesting analogy, but I'm afraid that is simply isn't true.

Recent studies have shown that well trained personnel (I think it was Incident Controller, aka Lead Fireman specifically) simply do not run all the possibilities in an emergency situation, they just look and act. The training allows them to adjust procedures as the reality of the situation emerges. The key thing being that they can never have any significant understanding of the problem domain in advance, only of the tools at their disposal. In tech support, the reverse is more often true: people know how to configure devices, but only use the diagnostic tools when they need to, and therefore only ever learn the bits that they have used so far.