Navigating links shouldn't be an issue assuming that the app hosting the web view is allowed to connect to the network.

But how about plugins loaded by the web view? I assume that's what's happening in my case. The web view is loading the Flash plugin, which in turn tries to access the file system.

That's not allowed, because the plugin inherits the entitlements of the parent app. The Flash plugin really can't believe that access to it's Library folder doesn't work so it tries and tries and tries sending the main thread into an endless loop blocking the complete app.