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eli_sennesh comments on The most important meta-skill - Less Wrong
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Can I give a counterexample? I think that way of learning things might help if you only need to apply the higher-level skills as you learned them, but if you need to develop or research those fields yourself, I've found you really do need the background.
As in, I have been bitten on the ass by my own choice not to double-major in mathematics in undergrad, thus resulting in my having to start climbing the towers of continuous probability and statistics/ML, abstract algebra, logic, real analysis, category theory, and topology in and after my MSc.
There's a big difference between the fundamentals, and the low-level practical applications. I think the latter is what estimator is referring to. You can't really make a breakthrough or do real research without a firm grasp of the fundamentals. But you definitely can make a breakthrough in, say, physics, without knowing the exact tensile strength of wood vs. steel. And yet, that type of "Applied Physics" was a pre-requisite at my school for the more advanced fields of physics that I was actually interested in.
Oh. Really? Dang.
You're right; you have to learn solid background for research. But still, it often makes sense to learn in the reversed order.