McFlabbergasty said:

Thanks, danaan. Pretty big oversight on my part. When Leia was talking about her father, was she referring to Bail Organa? It doesn't seem like she knew her father was Vader at that point.

I would assume so. I don't think anyone in the OT actually names Leia's foster-parents by first name.

Yet, at some point she likely does tell at least Luke that she is a foster-child, because in ROTJ Luke asks her about memories of her mother, adding "your real mother." So, it seems logical that "her father" in that holo-message would have been Bail, particularly since Anakin was Obi-Wan's apprentice, and thus not likely to end up in a position where he would have been commanding his mentor.