I think you are pointing out a related but slightly different problem. The question being asked is not "Does admitting wealthy students lead to higher alumni donations?" but rather "Does admitting legacy students lead to higher alumni donations?".

The latter one is what is being measured when they control for wealth and conclude that the practice of admitting based on legacy status does not result, in itself, with higher alumni donations. But like you said, when it becomes a means to admitting wealthier students, it can result in the former. But the two questions shouldn't be conflated and measuring them as distinct questions is why it's important to control for wealth in the methodology.