Often you see people claiming that since Google Webmaster Tools shows X, that web search much show the same thing. Or because there is a concern in Google Webmaster Tools, they are concerned about their rankings. Or that their rankings dropped down but Google Webmaster Tools shows no issues.
The big confusion out there is that Google Webmaster Tools and Google Web Search are independent. They may share some data but for the most part, they don't share algorithms, they don't share all the knowledge and they don't share a lot of details.
Google's John Mueller said so in a Google Webmaster Help thread:
Just to clarify what others have said -- adding the alternate versions of your sites helps us to show the right data in Webmaster Tools, but it doesn't change how your site is shown in search. Web-Search functions independently of Webmaster Tools, Webmaster Tools just displays the data from there.
At the same time, Google Webmaster Tools is an invaluable aid for webmasters and SEOs to diagnosis issues with web search. But it is fundamental to understand there is an underlining difference between the two. When you understand that, then using Google Webmaster Tools can be incredibly powerful.
For most of the readers here, this is known already.
Forum discussion at Google Webmaster Help.
