Of course not. For me Copyscape is nothing rather just a tool to determine percentage uniqueness. Most of the people think if the page is more unique than 50%, Google considers it unique. Of course Google knows that. But if Copyscape says 10-15% duplicate, then don't worry, since it's saying that for some words only.
Google has it's own version of a duplicate content(plagiarism) checker which is certainly more advanced than copyscape. Duplicate content would not necessarily be not indexed, it probably 'may' just not rank well as compared to the original version. As long as your site isn't full of scraped content, you need not worry.
For me there is no problem with duplicate and original content, it will be based on the entire reputation of the site.
Right, at worst, you'll see your article in the "omitted results" and you really have nothing too serious to worry about unless there are multiple version within your site, even then it wouldn't be that big of an issue unless it was happening a lot. There used to be a big rumor about duplicate content penalties, but it was just that.. a rumor.
Google crawls only when the content is unique and original, little % of duplication is not the matter of worry.
correct all it does is look for 3 word shingles in your text using Google's own API. If Google hasn't indexed ANYTHING that has ANY of your 3 word shingles in it, you 'pass'. It's a copyright theft detection tool, not a uniqueness detector. It's actually crap.