Google scans every URL that you submit to them in a Sitemap. It also scans URLs linked to the ones you submitted, and it may even scan all URLs linked to the home page.
You will definitely need to visit the HTML improvements section in Google Webmaster Tools for the website that supposedly has duplicate page titles and take note of all the URLs presented. Google is very accurate when it identifies URLs with duplicate titles.
If you have backups of the affected pages that are live, then that's the problem, because a backup copy is generally the same as a good copy.
For example, if you receive URLs grouped like the following (after expanding each duplicate title):
Then its a clear indication that you have made a backup copy of your work, but you need to make one version unavailable to the public either by placing it outside of the document root folder or changing permissions on the affected version so that the outside world has no access.
If after you done all that, you still notice problems, then I would give Google one to two weeks for it to process your site because Google is slow at updating some things. Another thing you can do to speed up Google's processing time is to select the gear icon in Google Webmaster Tools, and select site settings, and change Google's crawl rate and move the slider all the way to the right.