Another way to think about it:
Take the boat and anchor together as one object. When the anchor is on the boat or if it doesn't reach the bottom, the the whole weight of the 'object' will be supported by water, so there'll be no difference in water level between these 2 cases. When the anchor reaches the bottom, part of the weight of the 'object' will be be supported by the ground, so it will have a smaller displacement hence the water level will decrease.