index.html作为错误页面

I'm trying to use my index.html page as one of my ErrorDocument pages in Apache.

VERY SIMILAR to what this guy is doing here:
Index.php as custom error page

But without using PHP (server is running hot as it is).

What I've tried so far

Not much. Setting ErrorDocument 401 index.html puts Apache in an infinite deny loop.

Any way around this (again without PHP)?

Edit:

My .htaccess file at document root:

AuthUserFile /yep/this/path/exists/.htpasswd
AuthGroupFile /dev/null
AuthName "Please Enter Password"
AuthType Basic
Require valid-user

#ErrorDocument 500 "The server made a boo boo."
ErrorDocument 401 /index.html
#ErrorDocument 404 /missing.html
#ErrorDocument 404 "/cgi-bin/missing_handler.pl"
#ErrorDocument 402 http://www.example.com/subscription_info.html