First you need to know the user Apache is running with. Have a look at Apache's main configuracion file and look for the 'User' directive. In a Debian machine I have:
User www-data
RHEL can have httpd, or apache, or something similar. Let's say it's 'httpd' for this example.
Then have a look at the permissions of /var/cache/samba/winbindd_privileged, and note down the group of the directory. In the Moodle docs example (that you've pasted above), this is winbindd_priv, but RHEL will probably have another value. Let's say it's 'wbd_priv' for this example.
You need to make the Apache user ('httpd') a member of the 'wbd_priv' group. You can either use the GUI, or edit /etc/group, or use the 'adduser' command if it's available in RHEL. Editing /etc/group always works, so you just need to edit that file, search for the line that starts with (the number will differ, but this is not important):
wbd_priv:x:123:
(please note that there can be user account names after the ':' if there are already members of that group), and just add 'httpd' to the end of the user account list, separated by a comma like in the following example:
wbd_priv:x:123:oneuser,anotheruser,httpd
If this is the first member of the group, just add the user name after the ':', like this:
wbd_priv:x:123:httpd
Then you need to stop and start the Apache service. This is very important. Otherwise it won't work.
Saludos. Iñaki.