The problem of not experiencing a problem (using CentOS, and SElinux is enabled and in enforcing mode):
When I tried to view file2.html moved to /var/www/html, I do not get the forbidden message; the file is dumped to standard output fine.
When I examine the context of file2.html, it has etc_run_time_t rather than admin_home_t. But even when I use chcon to change that to admin_home_t to see if I can get the forbidden message, the file still dumps correctly.
Also a typo in 4:
$ sudo mv file2.html /var/www.html - should be /var/www/html