Bungie started talking about creating a "publishing group" at least as early as 3 years ago.
So yes, they have been trying to become a small publisher. They probably will continue to do that, considering they'll be releasing things on Xbox. It'll be interesting to see if games on Xbox from Destiny get any Sony / Playstation branding. I think that will be really telling of how independent Bungie really is.
Considering they don't belong to Playstation but rather Sony Interactive Entertainment, I don't see why they would have any Playstation branding. SIE? Absolutely.