The baby god event was never officially released, so this actually didn't canonically happen.
It was released. The Azure Flute and the event where you meet and battle Arceus in the Hall of Origin in DPPt was indeed never released, but this is different.
Arceus had various distributions in 2009-2010; the US one was at Toys R Us for example. Trading that legit Arceus to HGSS and then bringing it to the Ruins of Alph triggers this event which takes you to a special location where you can choose one egg of either Dialga, Palkia, or Giratina.
