Yes, 'Under the Queen's Umbrella' is based on a true story. It draws inspiration from historical events and the royal court of the Joseon Dynasty in Korea.
The hierarchical system within the palace, such as the roles of different court officials and the way the queen rules, could be inspired by true stories. Also, the importance placed on succession and the lengths the royals go to protect their lineage might have roots in real - life historical events. In addition, the cultural traditions and etiquettes shown in the series are likely to be based on the actual practices of the era.
The role of the queen in safeguarding her sons' positions is a key part from the true story. In the Joseon Dynasty, queens had to navigate complex political landscapes to ensure their progeny's future. Also, the strict hierarchy and courtly etiquette shown in the series are elements inspired by the true historical setting.