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Google Doodles have long been used by the company -- which uses its search page as its home page -- to brighten up on days which are special in the calendar. Unlike some search engines like Bing which maintains mostly consistent throughout the year, Google changes their logo into a fitting graphic for that day.
However, many took to the blogosphere and the forums to complain against a perceived 'Islamic reference' and a 'flag-burning' in a Doodle which was released on Veterans Day.
It is highly doubtful that Google would do this deliberately, regardless of the connotations. What does matter, however, is that quality assurance clearly did not vet this image enough to predict such a response from users of the service.
Google probably did nothing wrong, but the perception by the users due to lack of checks put themselves in a negative light.