It looks like Mozilla does use DNS to verify requests to join the list, at least.

  $ dig +short txt _psl.website.one @1.1.1.1
  "https://github.com/publicsuffix/list/pull/2625"

Doing this DNS in the browser in real-time would be a performance challenge, though. PSL affects the scope of cookies (github.io is on the PSL, so a.github.io can't set a cookie that b.github.io can read). So the relevant PSL needs to be known before the first HTTP response comes back.