Just a heads up folks, what was used to do this was a save game exploit. So far, there are currently 3 known save game exploits but so far, none of them can be used to play commercial games or flashcards, just homebrew. There are groups of people right now trying to find all the save game exploits they can.
Now the problem with save game exploits is Nintendo can release Firmware updates that can patch these exploits and delete them off the game cartridges making them useless. So even if an exploit was used to play games/homebrew, once it becomes public, its only a matter of time before a firmware update is made to prevent it.
So unless a custom firmware can be made, there is no long term solution to play pirated games or homebrew on the DSi. Now the problem is, the firmware is digitally signed making it near impossible for it to be hacked or a custom firmware to be used unless its signed by Nintendo.
So as it stands, the only feasible method to get Homebrew and backups to run on the DSi at the moment would be through hardware modification such as a modchip unless the digital signature used by Nintendo is cracked. Keep in mind that the DS Phat and DS Lite used RSA signatures for download play which has yet been cracked even after numerous attempts by various groups to do so.
NarinIt is possible for Nintendo to make a firmware update that will check the games before you even start them up for "unauthorized or compromised" saves and delete them before you even get a chance to use them. Also this method still requires a normal DS and a flashcard to edit the game saves or a device like the Action Replay DS to change and update the saves as well. So in the end, for the save exploit to work, you either need a DS Phat or Lite or third party hardware.