For some reason, when index.html is hosted in redmine, it has problems loading css and links.
Something with subfolders.

www/redmine/public/apidoc is visible as http://redmine/apidoc

When opened as
http://redmine/apidoc/index.html - it works (explicit file name)
http://redmine/apidoc - still gives index.html content, but all links points to
    http://redmine/, not http://redmine/apidoc/

I think there is something special about ruby-on-rails public folder.

Workarond is here!
I generate docs to 'apidoc.html' and redirect to it explicitly from index.html
