I thought that I might be thinking too much,
so I tested the game myself and then the save file got deleted.
I tried playing up to Slateport, because a patch of water tile near the pier in Slateport will appear glitch-y if the games are fake, from what I know that has something to do with memories.
Finally any Gen IV games will not detect the Pal Park system if the games are fake, and will also delete the save data of the fake games. From these check ups I decided that this is 100% counterfeit.
I'm actually very surprised that Nintendo hasn't taken the opportunity for easy money by putting gens. 1-3 up on the 3DS eshop. Of course it would take a bit of work to replace link cable with wifi, and if they wanted to add trading from the gen 3 games to DPPtHGSS (or maybe X and Y?) there would definitely be more work there, but I think the profits would be worth it for them.