The specific context is that of the surprising behavior of magnetic impurities in metals. When one writes down a quantum mechanical model to describe putting magnetic impurities into a metal, it turns out that one can leave out quite a lot (e.g. lattice structure) and still get the right answer.

Because the right answer is "so implausible given the simplicities" etc etc, one doesn't expect to get the right answer more than one way, so the insight from the simplest model necessary is sufficient.