There's no contradiction because they are different things.
To make a nandroid you need to install a custom recovery. You can do this if you can unlock the bootloader, which is not the same as rooting. A nandroid is a backup made using a custom recovery. You can also use the recovery to root the phone, and these are entirely separate things. If you have a custom recovery it's a good idea to take a nandroid before rooting, but it's not required.
Rooting means modifying the ROM to allow you to run user-installed apps with system privileges. The best way is to install a custom recovery and use that to flash a patch to root the phone, but not all phones have that option. Other methods, such as the various "rooting apps", do not give you the option of making a nandroid backup first, and if they do not install a recovery they do not let you make one at all, but they can still root the ROM.