The advice to developers is to ignore the concept of the Document Outline, simply because it has not been implemented in user agents and because of this, has a detrimental effect on users of AT.
Yes, it’s funny to read articles, books and so on extolling the new semantics, when in fact they don’t exist, because browsers and ATs for the most part ignore them. According to The Truth About HTML5, the creator of HTML5 doesn’t think those semantics will ever be implemented, and also doesn’t care!
I think, for the syndication use case, it’s rather sad that it’s not implemented. There was an attempt in IE…
To illustrate the browser behavior at this moment, I made 3 testpages: the good, the bad and the ugly. 
- With all H1 headers in nested <section>'s (and default H1 font-size): [U]html5-document-outline-1.htm[/U] (the bad)
- With H1, H2, H3 … headers in nested sections (& default font-sizes): [U]html5-document-outline-2.htm[/U] (the good)
- With all H1 headers in nested <section>'s (& specified H1 font-size): [U]html5-document-outline-3.htm[/U] (the ugly)
Using the latest version of Opera 12 (that’s v12.16 - all the later version numbers are early alpha versions of the replacement being built on webkit) the bad and ugly versions both look the same.
Yes, that is true. Thanks for the correction. The better to go over to the H1, H2, H3 … coding. 
I tested on Opera 17.0 for Windows desktop, the recommended latest stable version ([U]www.opera.com/docs/history[/U] as of 2013-10-08).
In the Opera download-section for desktops:
- Opera 17.0 is the latest stable for Windows and Mac.
- Opera 12.16 is the latest stable for Linux.
- Opera Next (now: 18.0) is the latest instable version (“developers edition”).
Internet Explorer versions:
- IE9, IE10, IE11: [U]Browsershots testpage html5-document-outline-1.htm[/U], all the same (and the same as FF23/24/25, Chrome30 and Opera17).
- IE9, IE10, IE11: [U]Browsershots testpage html5-document-outline-2.htm[/U], all the same (etc.).
- IE9, IE10, IE11: [U]Browsershots testpage html5-document-outline-3.htm[/U], all the same (etc).
To be complete, I added all version numbers in the text of the testpages.
On IE9 with JAWS 11? there was some funny outline-like but buggy behaviour, but later versions of JAWS and IE no longer do this.
Report on JAWS and NVDA (both Windows) on Firefox but similar behaviour reported for IE, by an SR user:
https://www.w3.org/Bugs/Public/show_bug.cgi?id=23545#c9
God what a mess. I was about to code up a site today with the new HTML5 structural elements, but then decided not to. They just suck, IMHO.
I’m coding a one-pager with <section>s, since for the content it does seem appropriate. But each section has either aria-label or aria-labelledby and first-child is a heading.