They lead by a large margin because they are buying their scores. People who have highly-cited papers are going to end up at very prestigious schools. For instance, imagine you publish a paper while at Oregon State on curing cancer and it gets 5,000 citations. Soon, you're offered a tenure-track position at Stanford. According to this scoring system, your cancer paper is now "associated" with Stanford as well as OSU, thus giving Stanford a big boost.
Yes, but when you are at Stanford you are then contributing your knowledge and skills to the Stanford research community. It doesn't matter whether you were at Stanford when you wrote the paper about curing cancer because a researcher at any institution will be teaching, writing, and contributing to them being a top research institution.
Sure, but if you're still performing top-notch research, your future publications at Stanford will show that. The goal is to rank schools based on which ones are the best research universities. The pressure to perform future research is lower for schools that can buy citations in this system.
