I'm also a trained physicist, spent some time in industry, and taught a college freshman math class for a semester a couple decades ago.

There's an interpretation that makes the reference answer correct. I didn't realize this until halfway through teaching the math class: Based on the lectures, textbook, and homework problems, you match the "form" of the problem with similar problems in the textbook, and apply the same algorithms to solve it. The students have some vague idea of this, referring to it as finding the "trick," but it's never explicitly explained to them.

I was glad for the interesting puzzles and good grades. But physics really came alive for me in the lab, where mother nature decides the conditions of the problem being solved.