Development Shack Technology Understood

Thanks to this article, I was able to fix my problem.

%{DOCUMENT_ROOT} was required for my redirects to work correctly:

RewriteCond %{DOCUMENT_ROOT}%{REQUEST_FILENAME} !-f

Before Apache 2.2:

RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^/(.+) /index.php [QSA,L]

Apache 2.2 and later:

RewriteCond %{DOCUMENT_ROOT}%{REQUEST_FILENAME} !-f
RewriteRule ^/(.+) /index.php [QSA,L]

The Apache 2.2 documentation is here: http://httpd.apache.org/docs/2.2/mod/mod_rewrite.html