What? DDG does not own Stack Overflow but it can run Stack Overflow's algorithm locally? Do you mean that Stack Overflow has it's search algorithm open sourced? I'm sorry, I don't quite get it.
Usually, the router search engine queries data from the second tier websites to get high quality results without having other websites' algorithms. Also there is another problem: how do you know which websites to go for given an arbitrary keywords? For example, when user searches for "cookie" on your search engine, where do you send the query to? How do you know if they are looking for food cookie or browser cookie?