you are dealing with the default behaviour for Twenty Eleven theme.
single posts do not have a sidebar.
for static pages, there is the ‘sidebar template’ page template which you seem to be using for your example page.
there are a few forum topics how to correct that – please try and use the forum search.
there is also a plugin http://wordpress.org/extend/plugins/twenty-eleven-theme-extensions/ available.
also, before you make any edits to Twenty Eleven, create a child theme to work with.
http://codex.wordpress.org/Child_Themes
do not edit the default theme Twenty Eleven directly.
if you get stuck with particular implementations, please post here again.
Many thanks, will follow up on those
Just to close this – problem solved with a child theme found here
I didn’t realise it was default behaviour – a feature, not a bug! – and hence my searches here and on Google were badly phrased.
Many thanks for your swift and patient assistance!