Evidence that Kairi was from Hallow Bastion lies in the library where that table is. That's the same table from her memory. DO NOT ARGUE THIS.
Okay, Sora unlocked his heart, thus freeing Kairi's. and the other princesses. He then was taken into darkness, and actually was it himself. Saved by Kairi, blah blah.
1) BHK wasn't a Princess.
2) He's not even a girl!
3) therefore he cannot have his heart connected by the blade.
Now, if we take it from the Namine/BHK point of view. Replica Riku had Namine as his charge. But wait... Riku is reminded of Kairi because she and Namine 'smell' the same. Thus, they may be connected.
There isn't quite enough to go on as of yet.