I don't know about Lin in particular, but as the Ivy League has gotten richer endowments, its sports teams have gotten better. It doesn't give out sports scholarships, but it gives out so much financial aid to middle class families now, that it makes sense for pretty smart and pretty athletic kids to play ball for the Ivy League: "Okay, UT El Paso, Iowa State, and Valparaiso are offering me full rides, or, for $5,000 per year I can go to Yale? Is this a trick question?"
I vaguely know a heavily recruited basketball player who enrolled in the last few years at a Very Famous Ivy League College. It was funny reading the ESPN interviews with him on Signing Day because the questions from the sportswriters were all framed as if all his ambitions were focused on the basketball court (Q. So, are you signing with Very Famous Ivy League College because you think you can help them win its first Ivy League title in 17 years? A. Uh, yeah, sure ... I mean, why not?), when his motivations for signing with VFILC were far more mature: He wants to go through life as a graduate of that Very Famous Ivy League College. It was like when I was at Rice in the 1970s, and the basketball coaching staff was alway scowling about how the 6'-11" backup center was just exploiting them to get a Rice engineering degree, always sneaking off to the library to work on differential equations.