Perhaps I am misunderstanding your case. I examined the site you refer to on iPhone 5, horizontal view. When navigating around the site, the address bar overlays or pushes the content up/down, depending on the user action.
Given that you are referring to a mobile web site, I may suggest that you try the native scrolling mode
of the mobile app - it relies on the built-in browser scroller, and in some cases works better for sites specifically.
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