The site-start.el file in emacs-20.4-5 has lines to load html-helper-mode
automatically when editing a *.html file.  The problem with this is that
html-helper-mode is not also included as part of the Emacs distribution,
which means that when I load a *.html file into Emacs, I get a file mode
specification error since Emacs can't load html-helper-mode.el.

I'll repeat here my previous complaint that it's obnoxious for an official
Emacs distribution to have all kinds of hacks in it which are not part of
standard Emacs.  Independent of that, if you insist on enabling
html-helper-mode in the RedHat emacs distribution, then you should include
html-helper-mode.el in the distribution.