Earlier quoted context omitted.
The privacy comes from the lack of tracking your interests and tailoring the search results to the preexisting interests. They just don't collect the private data in the first place.
That's one way of looking at it. Another way is that your PII like your IP hitting a MS server and searches being returned for that searcher are heavily correlated. They can't serve results like https://duckduckgo.com/?t=ftsa&q=shops+near+me&ia=web and return shops within miles of me without passing that info on. IIRC they pass the /24 of your IP, but all the same, not much better.
Does DDG provide Bing with your location (/24 or some other proxy) always, or only in the case of the local search in your example? Which seems like a minimal privacy violation (Can’t have “What’s nearby” and “I don’t want to tell you where I am”, but I get your beef; you want DDG to localize results instead of M$).