I mean, if it saved to the SD card, then nobody would be making a fuss about the single-save in the first place, because, well... you'd be able to back it up.
As shown in their "presentation video", however, the save is located on the cartridge itself and is detected as "corrupt" when used with a different game (rom), hence resulting in deletion.
I imagine a form of AP for newer games would be to check if the cartridge contains save data that belongs to another game, a circumstance otherwise not possible without modification to the cartridge.