[JadeNB]

> Essentially it boils down to: Just because two different models of computation can solve the same problems, does not mean that when augmented by the same oracle can solve the same problems (they can access the oracles in different ways).

Indeed, it was just the worry that something nasty like this could happen that made me weasel my initial definite assertion into the form of a question. Thank you for this informal explanation; it nicely complements openasocket's formal reference (https://news.ycombinator.com/item?id=12893077).

(Long-delayed post because "You are submitting too fast".)