It will be fine don't worry. All of your stuff is on the NNiD, you can easily re-download digital games you have already purchased off settings in the Eshop, and themes in the theme store. You just need to ask Nintendo to disconnect it first from your old 3DS. As you can't have the same NNiD on more than one 3DS. What these guys are referring to is when there was no NNiD yet on the 3DS. If you ever lost you 3DS, etc, your stuffed unless you had the serial number on the back of the 3DS and some proof depending.
For example one time back in 2011 - 2012 - 2013 (IDK now, it was too long ago) my friend's 3DS got ran over by a car. He rang up Nintendo and they added all the downloads he had on that 3DS to his brand new one for a small fee. He had tons of games so yeah. He got there in the end.