This is ultimately it. LinkedIn is now a large business, with a very large technology team. That they can spend the time and effort to optimize each platform should surprise absolutely no one.
But does it apply to you and me? In most cases, not even remotely.
I was recently involved with a team building a pretty amazing, full-featured web app (in the investor information space). Out of the pure magic of HTML, most of the app worked brilliantly not only on the desktop, but on the iPad, iPhone, Android devices, and so on. There were small edge issues, but overall it was simply brilliant, and for an investor on the go they could easily get an up to date snapshot of their portfolio with dynamic graphics, etc. It was a complete win for the web.
Yet even there a narrative erupted where some people pushed hard for native apps. That this tiny team of six developers that apparently needed to fracture to start building iOS, Android, etc, clients. It was utter insanity, and of course LinkedIn and Facebook both appeared as if they were the benchmarks we should follow ("See, they abandoned HTML! So should we").
Sure, if you have the resources of LinkedIn and Facebook, feel confident making those decisions. For the rest of us, HTML5 is pretty fracken amazing.