(I'm prepared for my faith to be rejected here, short of a "zk proof", which, despite my earlier regrettably general claim, does seem to exist on the open web (after some inspired googling, no less)... if you really give a damn, but these appear to be sensitive matters)

Scott's a careful guy so he skipped out saying explicitly what's "quantum" about Grover, only citing published lemmas where the question (obliquely) begs it.

Investigate in particular the section on open problems, where he can afford to be more forthcoming.

Here he mentions tight bounds on the "quantum depth" are unknown-- how about the classical? (Note Scott's repeated uh judicious use of quotes around quantum)

No royal road to (quantum) geometry, but nobody says out loud that there easily exists tyrannical(/classical) ones (:(

So,sorry, but I hope to have pointed in you in the general direction.

E: Feynman's level is a good threshold. What I cannot create, I do not understand