This is an inherent problem with web apps, since they're an app within an app. There are two different contexts fighting each other. Who's to say that Ctrl+S should save the app state or the page? Whatever we choose as the default, the non-default scenario would feel awkward when we need it.

I can think of two ways to solve this: (1) decouple apps from the browser frame or (2) use a special modifier key for app shortcuts (perhaps re-use the Windows key, e.g. Win+Ctrl+S).