Topic: Can't transfer account

Hey, so I recently lost my 3DS which had a digital copy of Pokémon Alpha Sapphire on it, fortunately I do have a backup of the SD card that was in it however this is useless.

Obviously to transfer accounts between DS's without the original system you need to contact Nintendo, so I did that and they asked for my current account which was fine and then the account linked to the new system (it had a separate network account on it because I didn't have enough SD card space for Pokémon Bank) which was also fine.

So up until now everythings fine except then they said that there are two other IDs associated with the 'new' system and that I'd need to provide details for them which I was unable to do.

It's understandable that they won't transfer it because I can't verify the other two accounts that have apparently been linked, however as far as I understand this should NOT be possible as it is only possible to link one Nintendo Network ID account at a time and if it were possible to link more that would negate the need to even call them in the first place.
I'm just super confused as to how two other accounts could have been linked when the reason I have to call them in the first place is because your NN ID can only be used on one console of each family at a time.
Any ideas as to what they mean by "there are two accounts, let's say, in the background"?

@autMia
As far as I remember it, you can link more than one NNID to a device, but you can't link an NNID to more than one device.

I.e. I bought a used Wii U with someone else's NNID on it. I then put a new NNID on it of my own but without deleting the first one because I wanted to be able to access the eshop purchases the previous owner had made.

I think Nintendo wants you to verify details of the previous NNIDs to show that the device is not stolen etc.

I'd recommend against buying used Nintendo hardware without getting full NNID details as part of the deal, or having the unit wiped.

Ah okay, I have no idea how the other two got on there.
I'll just have to replace the game and console then.
Thanks for your help!