The High King is the highest title within the dwarven hierarchy. Because it was the Stormshield clan that brought all of the dwarves into a unified nation and they have lead and protected the clans wisely for generations, the title has been hereditary.
However, the Hearthlords are not necessarily beholden to the High King. So long as the arrangment is of benefit to all of the clans, the Hearthlords lend their support to the High King and the dwarven nation. Should they feel that the Stone Crown is not aiding their clans as they feel it should, the Hearthlords every right to sever ties with Stonegaard.