Apache says DocumentRoot doesn't exist when it does or permission denied

Here's a tutorial approach to the SELinux case:
Find out if SELinux is active:

 $ sestatus
 SELinux status:                 enabled
 SELinuxfs mount:                /selinux
 Current mode:                   enforcing
 Mode from config file:          enforcing
 Policy version:                 24
 Policy from config file:        targeted

If so, some comparative checking might help. For instance, a server has a default DocumentRoot at /var/www/html, but we want it somewhere else like /path/to/document/root.
If SELinux is not actively messing with the resource, ls -dZ on the directory will show something like:

$ ls -dZ /path/to/document/root
? /path/to/document/root/

On the other hand, if SELinux contexts are applied, ls -dZ looks more like:

$ ls -dZ /path/to/document/root
drwxrws--x+ cfgadm cfgadmin system_u:object_r:file_t:s0 /path/to/documentroot

If we compare to a working DocumentRoot, it would look something like:

$ ls -dZ /var/www/html
drwxr-xr-x. root root system_u:object_r:httpd_sys_content_t:s0 /var/www/html

The _r and _t relate to -r (--role and -t (--type) arguments to chcon. Here is a cut-down man page:

NAME
   chcon - change file security context

SYNOPSIS
   chcon [OPTION]... CONTEXT FILE...
   chcon [OPTION]... [-u USER] [-r ROLE] [-l RANGE] [-t TYPE] FILE...
   chcon [OPTION]... --reference=RFILE FILE...

DESCRIPTION
   Change the security context of each FILE to CONTEXT.  With --reference,
   change the security context of each FILE to that of RFILE.

   --reference=RFILE
          use RFILE's security context rather than  specifying a CONTEXT value

   -R, --recursive
          operate on files and directories recursively

At first guess, the following might seem to work, but might not.

$ sudo chcon -R -t httpd_sys_content_t /path/to/document/root

If the web server still cannot see the DocumentRoot, note that the context matters all the way back to root:

$ sudo chcon -R -t httpd_sys_content_t /path/to/document
$ sudo chcon -R -t httpd_sys_content_t /path/to
$ sudo chcon -R -t httpd_sys_content_t /path

At this point, the web server can see the directory.
Yes, I learned the hard way tonight.