No, schools like Stanford care much more about getting the best students than playing the U.S. News rankings. They don't need to care about US news rankings. I think the most important graduate school rankings (times, arwu, nrc, etc) probably don't even look at admissions since they are ranking by the department quality which is mostly related to research.
When you go to open houses at the top ten-twenty schools, you see the same people over and over. There will
always be some people who got admitted to over 5 of these schools, even five top ten schools. These schools are not trying to distribute students between them, they are trying to get the best students to come. When you go to the open houses professors will ask you where you were admitted to so they can convince you to come to their school. UCSB or Stanford etc are not going to reject someone because they think they will get into other schools.