Is there actually a shipping user agent, screen reader or otherwise, that behaves this way? I could be wrong but I don't recall that they were ever particularly quick to make use of all the new markup we try and provide for them.
It reminds me of the battles about CSS vs Tables for layout where screen readers were always wheeled out as an argument for not using tables. Expect that all the shipping screen readers seemed to cope fairly well with tables.
(There are many ways in which your markup can break screen-readers but the issues are often more subtle and complex than 'use this tag or that tag' and require someone to actually test in a specific screen reader)
The iOS and OS X screenreader VoiceOver, for example. (JAWS, too, of course.)
It’s pretty cool actually: You can rotate with two fingers to switch between different ways of navigating the page: headline to headline, link to link, container to container, line to line and so on.
I suggest you try it out when you have the chance. (If you want you can test out HN to see how the experience here could be significantly improved if headline tags were used correctly.) Here is a short video if you can’t try yourself: http://www.youtube.com/watch?v=rxlxx6RXbs8
Do you really think accessibility advocates were asking everyone to correctly use headline tags for fun?
It reminds me of the battles about CSS vs Tables for layout where screen readers were always wheeled out as an argument for not using tables. Expect that all the shipping screen readers seemed to cope fairly well with tables.
(There are many ways in which your markup can break screen-readers but the issues are often more subtle and complex than 'use this tag or that tag' and require someone to actually test in a specific screen reader)