As far as I know, Williams doesn’t relax their distribution requirements for double-majors (except to the extent that major classes can fulfill the requirements in two divisions, rather than only one).
I suspect that the reason for the particularly high numbers of double-majors at both Williams and Amherst may be that neither school (unlike most LACs) offers traditional “minors”. So if a student wants to graduate with demonstrated knowledge of two fields, the double-major is the way to go. Conversely, the other schools listed would probably have higher numbers if you counted students graduating with a major + minor(s), instead of just double-majors.
Some schools (like Reed or Princeton) have mandatory thesis requirements that basically make double-majoring impossible. It isn’t really practical to research and write two theses during your senior year.