How to update a Drupal 6 website to latest release with drush?
As near as I can tell, drupal.org just removed all of the release xml for all contrib modules, and every version of Drupal 6.x core except for the latest release.

See the Drupal 6.x release xml for reference; all versions except 6.38 have been removed. Ah, look, the Views 6.x release xml contains content again!  Just a short while ago, it was gone.

Without the full release XML for Drupal 6 core, Drush cannot your existing versions; if it has no information about the current release, it gives up.  It is possible that this situation was accidental, and is being updated (c.f. the views release XML, which was recently restored).  Maybe this will start working again later.