The main argument against this statement is home screen icons. iOS and Android home screens, among others, do not feature, have not featured, and will not for months or possibly years, feature mobile web icons to launch websites in the browser of choice. Most or every icon on these home screens are native apps because mobile websites do not easily allow or make obvious that it's possible to have an app icon on the home screen. Thus, native will always win this battle.
When the day comes that it might be easier to see a mixture of native and web apps on the home screen, unless mobile web is faster than it currently is (meaning updating changing best practices, using excellent APIs like SW and designing for offline first access), users will STILL choose native over web when half or more than half the time they do exactly the same thing.
Native is here to stay for years to come unless the mobile web can offer a compelling reason to switch to browser based layouts. I'm cheering for the web to provide a better content experience but we're still a long way off and can expect web based layouts to be wrapped with native code and wrappers. Maybe web isn't the place for everything but a universal bytecode for everything is a dream that could be reality as long as progress is made.