Why can we not compare the coupling constants to chemically equivalent (but not identical) protons to determine magnetic equivalence?
The problem is that from the perspective of $\ce{H_{d}}$ and $\ce{H_{c}}$, $\ce{H_{a}}$ and $\ce{H_{b}}$ are different (you can tell which is which by their coupling constants). This difference means that there is a magnetic inequivalence between the two hydrogens $\ce{H_{a}}$ and $\ce{H_{b}}$, so there will be coupling between them.