The post to start the thread purposefully contained no commentary about the rating/ranking methods used. Fortunately you both noticed that the criteria may present a somewhat unclear or even distorted impression of schools.

schools had to have an average SAT score below 2000 or an average ACT score below 29 to be included on the main list.
Some may say these ratings/rankings are no longer a useful tool for identifying high-performing schools which may be a good "fit" for gifted, high-achieving pupils.

The Challenge Index is designed to identify schools that have done the best job in persuading average students to take college-level courses and tests.
Some may say it would be more accurate to report that the Challenge Index identifies "schools that have done the best job in persuading average the largest percentage of students to take college-level courses and tests", as the measure includes test administered, not courses taken and/or passed.

Equity and Excellence rate, which is the percentage of all graduating seniors, including those who never took an AP course, who had at least one score of 3 or above on at least one AP test sometime in high school. The nonprofit College Board, which oversees the AP program, invented this metric. It found that the average Equity and Excellence rate in 2014 was 21.6 percent.
Personally I'd like to see the math behind this. While described as "percentage of all graduating seniors... who", it may raise a question in some minds as to whether a senior who received >= 3 on more than 1 exam was counted only once when deriving the percentage (consistent with the written description), or whether each exam with a score >= 3 was included in deriving the percentage (which would be the number of exam scores >=3 as a percentage of graduating seniors, possibly more closely related to the "challenge index").

Because this measure includes "those who never took an AP course", might it include homeschool students who self-studied for an AP exam, therefore not be a measure of the school, per se?

College Board describes it this way:
AP Equity and Excellence Report: Report displaying the percentages of a school or district's entire 10th, 11th and 12th grade classes who scored a 3 or higher on at least one AP Exam and the percentage of the senior class that scored a 3 or higher on at least one AP Exam during high school.
The ratings/rankings seem to be a collective measure of equal outcomes, up to a ceiling (SAT <= 2000, ACT score of 29). Institutions with higher performance appear on the list of elite schools.