It is not uncommon for one search engine to ask another to remove links from their search engine database, it's still not uncommon when the two companies involved are Microsoft and Google either. Usually it involves the removal of a link to a website that displays or distributes some kind of copyrighted material, most of the time the system is handled automatically and a software is used to notify Google when a site is break the rules.
But software is only as good as its maker, it's never going to be perfect. Such as Microsoft's filing for link removal back in July 2012 when Microsoft was trying to cut the distribution of the leaked Windows 8 beta and was holding 65 websites accountable.
This is perfectly normal behaviour for either Microsoft or Google, of course they want to protect their interests on the internet. But it's when you look at some of the websites on the list that you start to raise eyebrows. Wikipedia, BBC, TechCrunch, Rotten Tomatoes... the list goes on. CNN, Buzzfeed, The Huffington Post, Washington Post, AMC Theaters and even a few websites belonging to the US government were breaking the law according to this removal request.
While its not the biggest problem in the world, the sites will have been unavailable on Google for a short while until someone realised the mistake, although I'm sure the websites involved didn't see a funny side to the issue.