I'm not sure how athletics is such a huge problem. The teams meeting in the BCS championship tonight have about 20 thousand undergraduates each. The football team, the largest surely on campus has something under 100 kids on scholarship, so about one half of one percent. Are there schools where it could be a problem? Perhaps. I've heard the complaint made about the Naval Academy.
The OP is focusing on the very-top-tier research Universities in the US. Most of these are private and much smaller than the large public schools which dominate NCAA championships.
For example, Princeton has only 4,500 undergrad so, as the author points out, athletes favored in admission make up an suprising large fraction of the class.
Likewise, legacy admissions has a big impact on the quality of Princeton admits, but probably not as much at the University of Oregon.
