Google and other SE's will try to figure out if there are duplicate URL issues, your step of using google tools removes an element of doubt for Googlebot. The bots/filters are fairly smart and will come across this kind of duplication often.
One of the main reasons to remove doubt/duplicate URLs/content is for links coming in which'll increase the prominence of your pages. It's generally better all round to not have duplicate URLs pointing to the same resource.
I will have to respectfully disagree with piatkow that "Nobody is going to link to non www unless you explicitly ask, even then half will 'correct' the link and put it in."
I have three domains that set to NOT use "www" and I have yet to have a single backlink or reference to these sites with "www" put back into it. With that said, I do have to usually delete "www" on submissions that have the string already started, i.e., "http://wwww"