Brown is in a 5-way tie for 8th place - so it is ranked 8-12, not 8. The move looks dramatic because the scores for the schools in that range are so close to each other. It would be hard to argue that it is statistically significant.
The peer assessment is best thought of as an attempt to measure the school’s “reputation within academia”, which may or may not correlate to a school’s “reputation within industry” or it’s “reputation within government” or it’s reputation within any other sector that a student may choose enter after finishing their education. This means that one should consider it’s potential relevance as well it’s potential accuracy.
It is really hard to argue that “reputation within academia” is the same as “academic quality” at the undergraduate level as academia appears to use different criteria for determining the “reputation” of LACs and Research Universities. If undergraduate academic quality equals ranking of doctoral programs, then the “academic quality” of Williams equals zero.
The more interesting experiment would be to take the peer assessment out of USNWR and see what happens…