They may not put it in those terms, but they do. They can tell when an app feels 'weird' or slow (be it actually slow or just higher latency). That depends a lot on the user base for the specific app in question. The more 'casual' the user base, the less it matters.
Being native also allows you to get functionality for free that other users may depend on. In OSX it translates to things like scripts, or more often, assistive devices, like screen readers.