Say you had two sections to your page… the content and the sidebar. OK say you put a H1 in the content section and a H1 in the sidebar. Is this somehow intended to give more Google emphasis to these headings…??

I mean, as opposed to simply having a H1 Page Heading with a H2 at the top of content area and a H2 at the top of the sidebar.

No matter which way I try to split the argument it really comes back to people just wanting to shout a little louder to Google through some construct like a logo or sidebar header. The information itself can always be marked up satisfactorily using a single H1 with sub-level H2 headings etc. I expect Google can interpret an appropriately set heading structure for its true meaning just fine that way without bending over to say “hey here’s multiple [shouting] top level headings - way important! Don’t miss my logo Mr Google”.