Starting RHEL7, Single user mode requires one to login with the root password as a security lockdown. However, in RHEL6/5 and earlier, single user mode by default would provide root shell. This is a security hole that most corporate would want to fix/harden to ensure there is no malice and compliance to much of regulatory requirements.
The following should help lock down Single User mode, so one would require to enter ROOT password in single user mode as well.
Edit the /etc/sysconfig/init file and change the following line
The following command should backup (/etc/sysconfig/init.bkp) a copy of your init and update the entry for you
# sudo sed -i.bkp 's/^SINGLE=\/sbin\/sushell/SINGLE=\/sbin\/sulogin/' /etc/sysconfig/init
Add the following to the /etc/inittab file
The following should do this for you:
# echo "su:S:wait:/sbin/sulogin" > /etc/inittab
And the next time you boot into single user, you will be prompted for a password.