Confirmed False!
Even though Nintendo 3DS ROMs do indeed have a unique game card header and signature, Nintendo would never ban the MAC addresses of any Nintendo 3DS from Nintendo Network. Why? Because anyone can use a game card in a different 3DS and so fourth. This means if Nintendo banned MAC addresses, just because they noticed the same header and signature used during online multiplayer at the same time, the person who has the game card that used to be owned by the person that had dumped the ROM would also end up being blocked by Nintendo, thinking it's another duplicate of the same header and signature. Which would make it completely unfair for anyone who plays online with a game card they bought from some store. And knowing Nintendo, they would never ban MAC addresses, just because they see the same header and signature used during online multiplayer.
The only times when they have to block MAC addresses of 3DS consoles... is when the person is using them for cheating in online multiplayer, such as using unlimited Bob-ombs in Mario Kart 7 while playing online.
*screenshot removed*
These people that have been so-called "banned" from online playability, would've probably been using some hacks during online multiplayer in either Pokémon X/Y/OR/AS, Mario Kart 7 or any games and ended up having their 3DS MAC address blocked. But I highly doubt they've been blocked from online multiplayer, I'd say that the person's router firewall probably has Nintendo Network's servers blocked by either domain name or IP address. That's usually what causes error code 002-0102. But also error code 002-0102 can also mean that Nintendo Network has blocked the 3DS's MAC address.
Also, I'd recommend spreading this message around. I'm sure it will help others to know that it's either that the person has been cheating in online multiplayer or has Nintendo Network's servers blocked on their routers' firewall (via IP address or domain name).