As a majority is it now belief that it was just mistaken for Tag Mode software/information being installed on the system?
After all the cartridges store information to be used while in tag mode in the system itself. So that when two 3DS cross paths they will exchange some sort of information or another. It's the only thing I can find that's been remotely similar and confirmed.
The Iwata Asks video which the information is from does say it in a way that can be mistaken if taken out of context, quite possibly partially an issue of an otherwise good translation. In the context though if that was the source of the rumour I can personally believe it to be false. As they were specifically talking about Tag Mode for the 3DS.
I mostly ask because some people still seem to be going more along the lines of that we can just install the cartridges. Personally at this moment in time I'm happier without installing games, as there's a lot more freedom in being able to use a certain game over multiple systems.
The carts contain eproms and/or flash mem for saving data. They could easily encode some sort of activation key, and then when you install the game, it could prompt you to create a unique password. That password could then be encrypted with the unique activation key on the eprom or flash, and then you could install that cartridge on any 3DS... but ONLY if you have the password. Which means the cart is still playable on any DS if resold, but not installable, and if your DS breaks, you have the password to install it on a new system.
That's the only way I see this working, but it is technically feasible.
I'm not 100% yet that this means save files would be stored on the system. It does have some uses for say sharing a game between multiple systems so say family members each get to play their own save. Would also allow for somewhat cheaper cartridge development if it didn't need to store save files.
Though considering some franchises like Pokemon would actually be hindered with not being able to move save files (Pokemon always gets locked). Because people typically take their old game and put it on another system to trade it to their new game.
Though they did mention Pokemon in the Tag Mode discussion. It's all open to interpretation I suppose about save files.