"you wouldn't want an app that renders html served by a server". I wouldn't because it would be (almost) impossible to render it differently in order to adapt it to the device ( since we're talking about native apps).

Logically, a rest API is a layer that is one level "before" html/css, since it only deals with data, and not rendering ( html needs data, not the other way around). Since web and native use different rendering technologies, the logical conclusion is to keep the common part of the stack at the data level, and not one level above it.