Trying to feed that query to a third-party service and then give users the results back adds significant risk that the third-party changes their API, changes their feature-set in an incompatible way, goes out of business, gets in a corporate fight with the search provider...
It's both cheaper and more convenient for the end-user if the search provider handles the mapping itself (in the absence of some kind of universal understood interface standard, complete with some kind of incentive to adhere to it).