Hmm... some things to consider:
-Subspace is from Sub-con, which is the land of dreams, and Kirby's home country is Dreamland. Brawl, like the SSB games before it, contains plenty of throwbacks to and inspirations by the Kirby series, which makes sense given that they were thought up by the same guy. Other games involving dream realms, such as Link's Awakening, are known to contain lots of improbable cameos by characters from other franchises, the Kirby series included. I might be grasping at straws with this one, but it's still something to think about.
-The fact that this is supposed to be a game within a game reeks of Kirby Super Star, which SSB is already known for having lots of concealed references to. I'm certain Sakurai was thinking of that when he decided to bill the Adventure Mode as it's own little game and give it a title.