This is really nonsense.
Native apps in general are testament to the UX failure that is Web standards and browsers. Think about the issues with CSS layout (e.g. Vertically centering) and (still) the relative poor performance of one page Web apps.
I heard someone else call native apps the new bookmarks. I think they're right. Think about the UX of a general purpose browser. You have to launch it then go to a site. That site's page is limited by the lowest common denominator of what a browser can do. It's also (at least) a two step process.
Native apps are generally task specific (e.g. Taking photos) or at least site specific (e.g. Facebook, instagram). This is much easier to use and understand.
That aside, Safari isn't what I'd call browser stagnation, certainly not to the degree Internet Explorer was back in the IE6 days.
What's more, Apple does a pretty good job of keeping users on the latest versions of iOS (compared to the likes of Samsung). The browser stagnation from OS version stagnation is far more damaging imho.