The update data is on the SD card, and most 3DS games that have updates don’t allow access to save files that are updated when the update data isn’t installed, but some allow access to other files that weren’t played on from an update or made on the current, updateless system if the game sports more than 1 save file.
As for not letting you play it period, it probably has to do with the game running a retrieval function when loading lists of replays or 3DS friends, and many computer programs run into problems when trying to retrieve data from a source that doesn’t exist, so it is likely that Nintendo’s 3DS convention contains the inability to access as a requirement for games that access the SD without one, but I haven’t a source for most of that.
I do, however, notice other 3DS games that react similarly. :P