That is very true. Advisor reputation flows out through his grad students. I'm known as one of "Mark's" students and that comes with significant baggage, both good and bad. In general his student have been very successful and when in certain circles that flowed back to him. Both in reputation and grant money. The grant money comes from people who know him or were his students and are working in the field and control research dollars that can flow to colleges.
It's a cool world, not without problems and inefficiencies, but it would be hard to create a better one that would be stable long-term.