"Browser-based" does not have to be synonymous with "web apps".
You could also see it as giving up control over your local cache of (photos, mails, apps, etc) in exchange for ease of use. This could replace "I want to play Angry Birds, so I download it and then run it" by "I want to play Angry Birds, so I click this button". Then, your device could download the app, if it was not already cached on your device, and run it.
That's exactly my point. The post I replied to objected to "everything in the browser" because "you cannot put everything on the web". I pointed out that A does not imply B.
For example, consider a browser with local storage that allows for running locally stored apps (written in SVG + JavaScript, Flash, NaCl, whatever). Such a device could run games, word processors,cetc, without a network connection.
You could also see it as giving up control over your local cache of (photos, mails, apps, etc) in exchange for ease of use. This could replace "I want to play Angry Birds, so I download it and then run it" by "I want to play Angry Birds, so I click this button". Then, your device could download the app, if it was not already cached on your device, and run it.