The above makes no sense
Sure it does.
Clerkship self-selection can come from multiple sources. One is the culture at the school -- if, as you speculate, something about SLS (school culture, professors, the clerkship office, etc) encourages relatively more people to want clerkships, then we would expect a greater percentage of the student body to have clerkships (because a higher percentage of "clerkship eligible" students will actually try to get clerkships rather than biglaw or something else). I'm not sure why it would be that the SLS school culture is more pro-clerkship than the Chicago school culture, and you haven't really pointed to any evidence that indicates that it would be. I think you're right that more people at SLS look for careers outside of the generic biglaw box (almost certainly in part because more of those semi-nontraditional careers are available coming from SLS), but that cuts the opposite way: students who pursue other post-graduate degrees, politics, thinktanks, etc are probably less likely to want clerkships than students who pursue biglaw (given that the further one strays from the traditional legal tracks, the less practical/resume-enhancing value the clerkship has).
A second source of clerkship self-selection comes from 0Ls choosing between schools. Different law schools have different reputations with regards to clerkships. Yale and Chicago have long had reputations for being clerkship overachievers: schools that send relatively more of their students to clerkships than their peers. Therefore, a student choosing between Harvard and Yale who has her heart set on clerking is probably more likely to choose Yale than a student with the same choice who has little interest in clerking. Although almost certainly many 0Ls change their minds about clerking -- some will decide that clerking sounds great while others will find a different passion -- it's also almost certain that many of these 0L interests are borne out in students' 2L and 3L career choices. Therefore, schools known for being good for clerking will attract more prospective clerks, and will thus have more 2Ls and 3Ls looking to clerk--e.g., the average clerk-eligible student will be more likely to actually want to clerk. My point was that we would expect Chicago, which has a reputation (probably deserved) for being a relatively good option for aspiring clerks, to have more 2Ls and 3Ls who want to clerk than a school (like Stanford) with no such reputation. Put another way, aspiring clerks choosing from the CCN bucket will disproportionately choose Chicago, while aspiring clerks choosing from the HYS bucket will disproportionately NOT choose Stanford -- leading to some clerkship selection bias at Chicago relative to Stanford. (That is, unless we think that there's something about admitted HYS students that make them more likely to clerk than admitted CCN students.)