It looks like Wikipedia agrees with you- Originally, "Yahoo Search" referred to a Yahoo-provided interface that sent queries to a searchable index of pages supplemented with its directory of websites. The results were presented to the user under the Yahoo! brand. Originally, none of the actual web crawling and data housing was done by Yahoo! itself. In 2001, the searchable index was powered by Inktomi and later was powered by Google until 2004, when Yahoo! Search became independent. On July 29, 2009, Microsoft and Yahoo! announced a deal in which Bing would henceforth power Yahoo! Search.[4]

I have no idea if this is still the case.