are you suggesting that DDG makes a call to Yahoo which then makes a call to Bing ("two times indirection")? Surely it's implemented differently than that, right?
It is definitely implemented differently than that. Yahoo has plenty of search engine knowledge and technology. There is surely some sort of process that inlines and caches any sort of query and result in Yahoo's backend. It's also fairly likely that they are using their own backend still for index storage and delivery, and they have some formal method of syncing the index from bing fairly regularly -- or even on demand for more long tail searches.
In other words, the most likely case where "double indirection" occurs is in very long tail searches that Yahoo has not seen recently.
Yahoo "had" plenty of own expertise - they created Hadoop afterall and used it for their own search engine. Until they closed it around 2010 for a deal with Microsoft Bing.
If Yahoo hosts the BOSS API on their servers or in on Microsoft servers as part of their deal, isn't known. As DDG recently started to provide the search results from a Yahoo sub-domain (and from Yahoo (or Microsoft?) data centers) to minimize the huge latency (that everyone hates) a little bit.
"To get access to the most relevant Yahoo technology, due to contractual obligations that call has to be associated with a Yahoo domain, in this case, duckduckgo-owned-server.yahoo.net." Of course they mention only the first part, as Yahoo itself relies on the Microsoft contract to access Bing search directly.
In other words, the most likely case where "double indirection" occurs is in very long tail searches that Yahoo has not seen recently.