Agree, and similar experience here: middling GPA from UConn because I worked 25-30 hours a week, partied too much and rarely attended class, but really high LSAT scores helped me (and also pegged me as a likely under-achiever for the schools I really wanted, including UConn Law, which later admitted me on transfer and gave me a scholarship).
The thing I wonder about the SATs and LSATs though is the extent to which they can be gamed with enough practice. There is no question that my Kaplan LSAT prep, and a great instructor, helped me improve my scores, but I also spent a ton of time doing practice tests, listening to the tapes, etc. To some extent, access to those resources may be limited; but I paid for it all myself with money I earned while working and going to school, so I'm not sure what privilege would have to do with it. Like anything, you just have to want it badly enough to put in the work.