This is a great question that the book does not entirely explain. This one subject of the mechanism that caused the crust to sink, like so many other individual subjects discussed in the book, could easily employ the space of an entire chapter if one were to add detail to the process. An attempt will be made here to shorten that explanation, but still present the necessary components.
There are multiple forces involved in the process including gravity and centrifugal force. Gravity pulls things toward the center of an object and the centrifugal force from the spinning object pulls things away from the center of the object. The component that adds to the ability of continents to float on the surface of the underground oceans is displacement. Much like a very large ship made of steel can float on the ocean.
All of these components, and others, were in perfect balance before the comet flyby and are now again today. A fourth component came into play as the unbalancing process began which is the answer to your question and it is a simple matter of density. The crust is more dense than water. When the crust sunk, it displaced the less dense water. We use the analogy of a bucket of water swinging in a circle over our head; the water stays in the bottom of the bucket. Drop a rock in the bucket of water and it sinks to the bottom, under the water because it is denser than the water. The bucket analogy demonstrates centrifugal force well, but the force of gravity is a little harder to see, although it is absolutely there and exerts a greater force on a higher density object when the equilibrium changes.
To put it another way, the water, crust, and everything else all basically slowed at the same rate. The reason the crust sunk was its density in relation to the water beneath it. Centrifugal and gravitational forces affect objects differently based on their density.