And I misspoke about the bang syntax: it actually runs a search on the target website. If you search for "foobar !g" on DDG, it redirects you to this page: https://encrypted.google.com/search?hl=en&q=foobar. Same as "kitten video !yt" redirs to https://www.youtube.com/results?search_query=kitten%20video.
edit: I misread your comment about goog's site search indexing vs a site's native search. That is entirely site dependent. And it's still only a "kitten videos site:youtube.com !g" away in DDG.
And I misspoke about the bang syntax: it actually runs a search on the target website. If you search for "foobar !g" on DDG, it redirects you to this page: https://encrypted.google.com/search?hl=en&q=foobar. Same as "kitten video !yt" redirs to https://www.youtube.com/results?search_query=kitten%20video.
edit: I misread your comment about goog's site search indexing vs a site's native search. That is entirely site dependent. And it's still only a "kitten videos site:youtube.com !g" away in DDG.