I can't say the YouTube video really helps in terms of the problems we're seeing on the One X. For the webpage he just went to the home screen and back in. For the Play Store he went to the home screen, then opened S Voice but did nothing data intensive with it, went back home, then back to the Play Store. I'm pretty sure I could recreate this on my One X.
What I'd love to see is loading the page, switching directly to the Play Store and heading to an app, switching directly back to the browser (and seeing if the page is still there), and using the browser to search for info on the app (just an example). I'd then like to make sure that when he switches directly back to the Play Store that we're still on the app page. I don't know why but the going back to the home screen thing really bothered me haha it's like clicking Show Desktop every time.