How can the rule "certainty is not removed by doubt, and the default state of things is purity" be reconciled with the Maliki saying regarding the obligation to sprinkle a place with water when there is doubt about its impurity, especially for someone suffering from obsessive-compulsive disorder related to purity?

Certainty is not dispelled by doubt, and the default state of things is purity. The Malikis made it obligatory to sprinkle water (nadh) on something suspected of being touched by impurity, to ward off whispering (waswasa), not to remove impurity. They based this on the action of the Prophet, peace and blessings be upon him, who sprinkled water on a mat that was doubted, and on the saying of Umar ibn al-Khattab: "I wash what I see, and I sprinkle what I do not see." Sprinkling (nadh) is a light sprinkling of water, and it is not a removal of impurity, but rather a means to dispel doubt and reassure oneself. Similarly, the Prophet's command to wash the hands after sleeping, before putting them into a vessel, is due to doubt. The majority of scholars understood this command as recommended, while Imam Ahmad understood it as obligatory for sleep during the night.