That would be the case for a federal election, for which Bush v Gore is precedent. However, I believe WA State law provides for such a partial recount.
Washington law requires that if the winner is flipped by doing a partial manual recount, then the entire state will be manually recounted. IOW if Gregoire wins on partial recount, the entire state recount will be done, I believe at tax payer expense.
Bush v. Gore established that partial recounts were violations of the 14th amendment. That would apply across the board -- federal, state, local.