There are probably myriad settings I needed to include here, but I'm
kind of drawing a blank about which ones.

Some basics are:

OS: Running debian jessie (fully updated) running in Vbox vm on
Solaris-11 host (openindiana/hipster)

emacs-version:
  GNU Emacs 26.0.50.1 (x86_64-unknown-linux-gnu, \
      X toolkit, Xaw3d scroll bars) of 2017-01-01
 (From local git branch of emacs pulled today (170725))
(The `unknown linux' mentioned above is debian jessie)

From gnus:
  (setq mm-automatic-display (remove "text/html" mm-automatic-display)
        mm-discouraged-alternatives '("text/html" "text/richtext"))

  (setq mm-inline-text-html-with-images t)

What else do I need to post?

Included is screengrab showing what I see when opening an html message
from Verizon.