I must either change that root so that it becomes a user with remote privileges or add another user named 'root'@'<remote address or `%` for any address>' which is what I did.
Where is your second option implied by using either? You should never do the above. You should create a seperate user, with minimum required privileges. You should
never mess with the root account for MySQL.
The FAQ states this for a purpose:
"you must also create a user who is allowed to login from those systems"
It never stated that you should have modified your root user. It explicitly told you to create a user. I seriously suggest you revert your changes as your current configuration is a high security risk.
Please follow these instructions to create users:
http://wiki.contribs.org/MySQL#Creating_MySQL_user.28s.29and fore more details look through the MySQL manual.
SME makes it impossible for any user named root to access MySQL remotely. This is entirely different and deserves a more explicit explanation in the documentation.
That is not true and you show no proof for such a bold statement. You most likely have done something wrong or forgotten something as this does work. Perhaps you forgot to update the privileges or use the proper password?