Your savings is what did you in and yes it is true there is more variability at higher incomes. I plugged in $300,000 income into the calculator with very little savings and it gave me the $30K grant per year but for sure if your family is upper middle class or wealthy you are going to pay higher tuition for a Williams or similar school than at a state school.
My take is that if your family makes less than $100K and doesn't have a large you are going to be far better off in terms of any student debt at Williams than almost any state school. This is true with exceptions up to $150K in household income assuming you don't have a big 529 plan (parents max out your Roth before contributing to a 529, it can be used for education expenses and retirement accounts gets counted at a lower rate when it comes to financial aid).
Most state universities only give scholarships for tuition not for room and board whereas Williams will take into account the full cost of school including room, board, books, and other expenses in their grant formula.
Also $80K for Williams is the all in cost, it's high but UCLA is $36K, Umass $32K.
If your household income is $50K to $75K the average cost of UCLA after aid is $13K per year, at Williams the average cost would be $7K, everything else would be covered by a grant.
$75K to $110K at Williams and you're annual cost after aid would average $14.6K at UCLA it would be $19.5 according to the From US Dept of Education (IPEDS) calculator.
Today many state schools are under financial pressure and a lot of smart students don't get full rides just for academics. My wife was valedictorian of her high school class and a national merit finalist wanted to stay close to home so she went to University of California at Santa Barbara. She got a partial academic scholarship but no where close to a full ride. As her family income was high, she did in fact pay significantly less for her UC education than had she gone to Harvard where she was also accepted but her state school education wasn't close to being free.