You do not need SNMP R/W to backup configs. You only need SNMP R/O. But it sounds like your problem is related to the username and password.
If you are monitoring your node successfully in NPM using SNMP, then your SNMP settings are correct. You don't need to do anything with it.
So the easiest way to check if you can successfully back up a node is to go to Node Management, select the Node and click on Edit Properties. Then scroll down to this section.
Fill out the settings you want to use (like username and password and Request Configs Using) and then click on Test. If it comes back with Test Successful! then you know your settings are correct and now NCM will backup your configs.
I use TELNET for all my general config backups.
