Yeah, exactly that, it depends on the neck to body angle.
On most Gibsons, hardtail PRS models and similar guitars the neck is pitched back a few degrees so the strings are nowhere near parallel with the top of the body. Then you need slanted rings so the pickups can sit parallel to the strings.
On most Fenders, tremolo PRS models and pretty much anything with a bolt-on neck, the neck isn't pitched back at all so the strings are parallel with the top of the body (in practice there's a slight angle, otherwise the strings would be buzzing like crazy!). That's when you'd need flat rings, although in practice many guitars of this type have scratchplates or pickups screwed directly to the body.
If the guitar has a Floyd Rose style trem, because it's taller than a Fender (or PRS) trem it usually needs to be recessed into the body to keep the strings low. The alternative, again, would be to have the neck slightly angled back so the strings sit higher at the bridge.