The modifications I made a few years ago to add the sidebar to all pages messes up the responsive design. So I'm try to use the widget add-on to a clean style to get this done.
I created a style ("mobile") for each site that has no custom modifications. It is this style that the responsive design works, but I noticed the issue mentioned above.
Pretty sure that's the way that responsive works.. the sidebar (which contains lower priority information) is displayed at the bottom of the site on responsive.
But, as for obscuring it.. I didn't have that issue on my iPhone 6 using IOS 9.0.2 (jailbroke) with Chrome.