Good question--if they want power-raking, I say do it. If you don't like it you can always use one of those organic enzyme products to eat the thatch--probably don't work--but a lot easier to apply. You are probably wise to explain how an early short mowing is the best way to stimulate quick green up. Keep in mind some types of grass ( like the high-quality Kentucky bluegrasses) just simply green up very slowly--its their nature. Maybe they do better in the heat of summer.
Actually, I am not a fan of aeration. Customer has a good point--in 6 weeks it looks the same.