So I finally found the issue causing the WebView not to render. I am starting and stopping the animation of a drawable inside the WebViewClient of my WebView. This drawable is simply a refresh button that rotates when the page is loading... simple right?
Well in the non-fullscreen mode of the browser, the rotating drawable and the WebView are both children of the same parent, whereas in the fullscreen mode, the drawable becomes a child of the WebView. Somehow, by starting the animation when the page is loading and stopping it when it's done (in fullscreen), the application decides that the rotating drawable is what needs all the drawing power and the WebView never draws. When in fullscreen mode and the drawable becomes a child of the WebView, the WebView then has a higher rendering priority than the drawable and it draws fine.
The moral of the story is... WebViews like to be the highest priority view to be drawn. If there are other views that get greater priority, they won't draw correctly.
I'm no expert on animations, so I need to rethink how I'm animating the drawable now so as to not interrupt the WebView.
Hopefully that made sense. Thanks for reading.