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It doesn't seem like that necessarily conflicts with native apps dominating smartphone usage - there's a significant number of use cases where a user wouldn't use an app, such as reading news articles linked from an app like Feedly. Mobile use is growing fast enough (and desktop is flat to shrinking) that a doubling of web usage may just represent the overall shift in usage patterns (i.e. desktop consumption of web moving to mobile.)

Slide 16 supports the apps over native story: app revenue is dominating browser advertising on an increasing basis.

Embedded browsers within native apps likely add serious growth for web usage. E.g. Facebook native app is hugely popular, and sends a lot of traffic to a lot of websites within the app's browser.

I think everybody's stats are getting thrown out by the tendency of iOS browsers (at least) to refresh page just about every time app or tab focus changes.

I suspect that's unlikely - most analytics are focused on time-based sessions, where refreshes don't matter.