Beaver don't care if the river floods or not. They flood the timber because their principle means of transportation is water. They need the water to transport green limbs for storage in their underwater cashe of winter food. They are also vulnerable on land to predators, so the farther the water goes up to the trees, the safer they are.
Tell him not to worry though. As soon as all the trees around the lake are dead and gone, they will move on to somewhere else!
My dads property is along a creek. Every few years the beaver move up the creek looking for new food sources. Kind of like a swarm of locust on a wheat field. The neighbor on the other side of the creek did not want them trapped. He liked to "watch them". He even stold all my traps once. One year they hit him first. Before he knew it, they had cut down or killed most all of his big trees along the creek. Then he called dad and said "we've got to do something about these beavers". Dad told him if he'd buy me some new traps that we'd be glad to trap them out for him. Got 4 brand new 330's out of the deal.