There is no proof that DuckDuckGo operates as advertised. (There never is, on the web.) However, that is the wrong question. DuckDuckGo is very clear in its privacy policy. DuckDuckGo says it doesn't track you, it doesn't send your searches to other sites, by default it does not use any cookies, it does not collect personal information, it does not log your IP address or other information about your computer that may be sent automatically with your searches, it doesn't store any personal information at all. Those are pretty strong promises, with no weasel-wording. And, as far as I can see, DuckDuckGo's privacy policy seems like a model privacy policy. It is a model of clarity, plain language, and lack of legal obfuscation. And privacy policies have bite. The FTC has filed lawsuits after companies that violate their own advertised privacy policy. (Not just little companies you've never heard of: They even went after Facebook!) The way privacy law works in the US is, basically, there are almost no privacy rules that restrict what information web sites can collect -- except that if they have a privacy policy, they must abide by it. Breaching your own privacy policy may be fraud, which is illegal. Also, violating your own privacy policy represents "unfair or deceptive acts or practices", and the FTC is empowered to pursue anyone who engages in "unfair or deceptive acts or practices" in court. DuckDuckGo would be pretty dumb to breach their own privacy policy; their privacy policy is clear and unambiguous and leaves them little wiggle room. No, I don't think that DuckDuckGo is a scam. I think that's crazy talk. Given the incentives and legal regime, I think you should assume DuckDuckGo follows their own privacy policies, until you find any information to the contrary.
There was also a claim that DuckDuckGo will not index Russian websites, or will put them below other websites.
So I don't think DuckDuckGo is anonymous anymore.